{"id":"https://openalex.org/W2015947409","doi":"https://doi.org/10.1137/0614012","title":"More Matrix Forms of the Arithmetic-Geometric Mean Inequality","display_name":"More Matrix Forms of the Arithmetic-Geometric Mean Inequality","publication_year":1993,"publication_date":"1993-01-01","ids":{"openalex":"https://openalex.org/W2015947409","doi":"https://doi.org/10.1137/0614012","mag":"2015947409"},"language":"en","primary_location":{"id":"doi:10.1137/0614012","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0614012","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5103094159","display_name":"Rajendra Bhatia","orcid":"https://orcid.org/0000-0002-1959-0691"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rajendra Bhatia","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5061822718","display_name":"Chandler Davis","orcid":"https://orcid.org/0000-0002-1198-8056"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chandler Davis","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.2156,"has_fulltext":false,"cited_by_count":191,"citation_normalized_percentile":{"value":0.95640939,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":"14","issue":"1","first_page":"132","last_page":"136"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9976999759674072,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9976999759674072,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11564","display_name":"Mathematical Inequalities and Applications","score":0.9976000189781189,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9886000156402588,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7744604349136353},{"id":"https://openalex.org/keywords/matrix-norm","display_name":"Matrix norm","score":0.7240244150161743},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.5934012532234192},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5912604928016663},{"id":"https://openalex.org/keywords/linear-algebra","display_name":"Linear algebra","score":0.5163296461105347},{"id":"https://openalex.org/keywords/hadamard-product","display_name":"Hadamard product","score":0.5107913017272949},{"id":"https://openalex.org/keywords/singular-value","display_name":"Singular value","score":0.4817228615283966},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.46949127316474915},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.45761221647262573},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.40916502475738525},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3936437964439392},{"id":"https://openalex.org/keywords/hadamard-transform","display_name":"Hadamard transform","score":0.28154855966567993},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.21602189540863037},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12505587935447693},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.10737431049346924}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7744604349136353},{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.7240244150161743},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5934012532234192},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5912604928016663},{"id":"https://openalex.org/C139352143","wikidata":"https://www.wikidata.org/wiki/Q82571","display_name":"Linear algebra","level":2,"score":0.5163296461105347},{"id":"https://openalex.org/C90230998","wikidata":"https://www.wikidata.org/wiki/Q3406746","display_name":"Hadamard product","level":3,"score":0.5107913017272949},{"id":"https://openalex.org/C109282560","wikidata":"https://www.wikidata.org/wiki/Q4166054","display_name":"Singular value","level":3,"score":0.4817228615283966},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.46949127316474915},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.45761221647262573},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.40916502475738525},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3936437964439392},{"id":"https://openalex.org/C60292330","wikidata":"https://www.wikidata.org/wiki/Q1014065","display_name":"Hadamard transform","level":2,"score":0.28154855966567993},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21602189540863037},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12505587935447693},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.10737431049346924},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0614012","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0614012","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W1588963622","https://openalex.org/W1966112258","https://openalex.org/W2021794340","https://openalex.org/W2023267838","https://openalex.org/W2054560172","https://openalex.org/W2164818780"],"related_works":["https://openalex.org/W4366831400","https://openalex.org/W2158044763","https://openalex.org/W4298234822","https://openalex.org/W2782047334","https://openalex.org/W3206304544","https://openalex.org/W3017414697","https://openalex.org/W2006601391","https://openalex.org/W2962791795","https://openalex.org/W2409839127","https://openalex.org/W1554365047"],"abstract_inverted_index":{"Previous":[0,226],"article":[1,3,227,229],"Next":[2,228],"More":[4,757,1058],"Matrix":[5,122,604,1610,1612,1615,1783,1809,2022,2217],"Forms":[6],"of":[7,57,115,118,140,194,236,260,266,293,320,343,364,385,389,402,427,433,461,482,498,503,565,570,621,645,665,674,691,700,721,762,847,872,916,931,940,965,982,990,1008,1025,1029,1042,1081,1084,1119,1121,1124,1126,1141,1147,1166,1201,1221,1225,1241,1244,1246,1263,1265,1386,1408,1423,1427,1514,1516,1570,1595,1657,1673,1827,1831,1869,1894,1951,1956,1979,2001,2055,2117],"the":[8,112,403,428,434,622,646,692,697,718,739,848,960,983,1142,1202,1364,1424,1445,1467,1568,1571,1752,1888,1935,1980,2151],"Arithmetic-Geometric":[9],"Mean":[10,312,316,606,1533,1711,1995],"InequalityRajendra":[11],"Bhatia":[12,16,106,523,1803],"and":[13,17,34,64,107,146,162,169,192,233,241,248,262,313,340,382,406,415,463,484,501,506,524,549,572,591,625,633,651,688,702,723,765,779,786,804,809,827,831,845,850,874,892,897,909,918,933,942,962,967,1012,1040,1045,1062,1106,1128,1149,1184,1188,1206,1248,1267,1284,1288,1309,1326,1389,1405,1410,1429,1450,1471,1491,1495,1518,1532,1554,1575,1590,1598,1617,1633,1639,1678,1698,1713,1717,1738,1756,1761,1785,1799,1804,1811,1847,1850,1865,1871,1891,1896,1916,1931,1937,1970,1996,2024,2039,2073,2085,2104,2121,2137,2162,2174,2180,2199,2219,2236,2257],"Chandler":[14,18,133,156,2118],"DavisRajendra":[15],"Davishttps://doi.org/10.1137/0614012PDFBibTexSections":[19],"ToolsAdd":[20],"to":[21,66,172,290,410,588,717,738,868,959,1444,1466],"favoritesExport":[22],"CitationTrack":[23],"CitationsEmail":[24],"SectionsAboutAbstractFor":[25],"arbitrary":[26],"$n":[27],"\\times":[28],"n$":[29],"matrices":[30,63,288,339,381,1712],"A,":[31],"B,":[32],"X,":[33],"for":[35,84,138,285,307,336,360,378,457,479,543,628,649,696,743,782,824,914,936,956,986,1006,1065,1145,1163,1219,1261,1305,1487,1510,1593,1734,1776,1825,1862,1954,1973,1999,2015,2052,2070,2080,2099,2155,2234,2255],"every":[36,2156],"unitarily":[37,429,458,629,1488,1511,1866,2081,2157],"invariant":[38,224,357,430,459,630,1489,1512,1867,2082,2158,2241],"norm,":[39],"it":[40],"is":[41],"proved":[42],"that":[43],"$2|||A^":[44],"*":[45,48,52],"XB|||\\leqq":[46],"|||AA^":[47],"X":[49],"+":[50],"XBB^":[51],"|||$.[1]":[53],"T.":[54],"Ando,":[55],"Concavity":[56],"certain":[58,499,980],"maps":[59,800,888,1180],"on":[60,453,801,889,1101,1181,1281,1782,1808,1887,1910,1934,2021,2150,2216],"positive":[61,286,337,379,744,937,987,1222],"definite":[62,1223,1671],"applications":[65,171,209],"Hadamard":[67,2071,2196],"products,":[68],"Linear":[69,144],"Algebra":[70,145,247,632,808,830,896,1011,1105,1187,1205,1287,1308,1449,1470,1494,1553,1638,1677,1697,1716,1737,1760,1849,1915,2038,2084,2103,2120,2136,2161,2179,2198],"Appl.,":[71,124,147],"26":[72,599],"(1979),":[73],"203\u2013241":[74],"10.1016/0024-3795(79)90179-4":[75],"80f:15023":[76],"0495.15018":[77],"CrossrefISIGoogle":[78,154,220],"Scholar[2]":[79],"Rajendra":[80,105,522],"Bhatia,":[81],"Perturbation":[82],"bounds":[83,542,2069],"matrix":[85,361,585,1306,1446,1675,1692,1911,2159,2177],"eigenvalues,":[86],"Pitman":[87],"Research":[88],"Notes":[89,1909],"in":[90,210,438,509,528,608,853,1342,1550,1635,1654,1940,2176],"Mathematics":[91,198,2259],"Series,":[92,677],"Vol.":[93,251,271,295,324,346,366,391,418,441,465,486,512,531,553,574,594,610,636,654,678,704,725,747,767,789,812,834,855,877,900,920,944,969,992,1015,1031,1048,1069,1089,1109,1130,1151,1169,1191,1209,1228,1250,1269,1291,1312,1329,1350,1368,1392,1412,1431,1453,1474,1498,1520,1537,1557,1578,1600,1621,1642,1660,1681,1701,1720,1741,1764,1787,1813,1834,1853,1874,1899,1919,1959,1984,2004,2026,2042,2058,2088,2107,2124,2140,2165,2183,2202],"162,":[94],"Longman":[95],"Scientific":[96],"&":[97,2246],"Technical,":[98],"Harlow,":[99],"1987viii+129":[100],"88k:15020":[101],"0696.15013":[102],"Google":[103,202],"Scholar[3]":[104],",":[108,158,163],"Fuad":[109],"Kittaneh,":[110],"On":[111,777,1301,1378,1484,1567,2132],"singular":[113,825,1302,1492,1731,1892],"values":[114,826,1893],"a":[116,141,291,308,341,383,666,869,1082,1932],"product":[117,1864,1890],"operators,":[119,412],"SIAM":[120,176],"J.":[121,177,205,213],"Anal.":[123],"11":[125,470,1663],"(1990),":[126],"272\u2013277":[127],"10.1137/0611018":[128],"90m:47033":[129],"0704.47014":[130],"LinkISIGoogle":[131,186],"Scholar[4]":[132],"Davis,":[134,157],"An":[135,820,1002,1844,2191],"extremal":[136],"problem":[137],"extensions":[139],"sesquilinear":[142],"form,":[143],"13":[148,1074],"(1976),":[149],"91\u2013102":[150],"10.1016/0024-3795(76)90046-X":[151],"52:15068":[152],"0326.15012":[153],"Scholar[5]":[155],"W.":[159],"M.":[160],"Kahan":[161],"H.":[164],"F.":[165],"Weinberger,":[166],"Norm-preserving":[167],"dilations":[168],"their":[170],"optimal":[173,1343],"error":[174],"bounds,":[175],"Numer.":[178],"Anal.,":[179],"19":[180,396],"(1982),":[181],"445\u2013469":[182],"10.1137/0719029":[183],"84b:47010":[184],"0491.47003":[185],"Scholar[6]":[187],"A.":[188],"McIntosh,":[189],"Heinz":[190,314,507,544,671,719,780,851,911,934,963,984,1043,1122,1143,1203,1242,1323,1361,1383,1403,1425,1572,1591,1735],"inequalities":[191,265,335,359,377,409,456,478,586,627,648,715,736,742,781,806,866,894,913,935,955,1064,1123,1144,1218,1243,1304,1362,1442,1464,1486,1509,1549,1592,1634,1653,1824,1972,2175],"perturbation":[193],"spectral":[195],"families,":[196],"Macquarie":[197],"Reports,":[199],"79-0006,":[200],"1979":[201],"Scholar[7]":[203],"Colin":[204],"Thompson,":[206],"Inequality":[207,284],"with":[208,413,1346,2101],"statistical":[211],"mechanics,":[212],"Mathematical":[214,763,1087,1226,1535,1596,1982],"Phys.,":[215],"6":[216,657],"(1965),":[217],"1812\u20131813":[218],"32:7110":[219],"ScholarKeywordsgeometric":[221],"meansingular":[222,2239],"valuesunitarily":[223,2240],"norm":[225,283,358,408,431,805,893,1185,1548,1636,1823,1977],"FiguresRelatedReferencesCited":[230],"ByDetails":[231],"Norm":[232,334,376,714,735,954,1441,1652,2050,2068],"numerical":[234,263],"radius":[235,264],"single":[237],"operators":[238,650,957,1632,1975,2100],"through":[239],"tools":[240],"techniques":[242],"from":[243],"multivariable":[244],"operator":[245,759,802,890,1182,1324,1655,1758,1828,1845,2036,2134],"theoryLinear":[246,2178],"its":[249,634,810,828,832,898,1013,1107,1189,1207,1289,1310,1406,1451,1472,1496,1555,1640,1679,1699,1718,1739,1757,1762,1851,1917,2040,2086,2105,2122,2138,2163,2181,2200],"Applications,":[250,464,485,573,635,703,724,766,811,833,899,919,943,968,1014,1108,1129,1150,1190,1208,1249,1268,1290,1311,1411,1430,1452,1473,1497,1519,1556,1599,1641,1680,1700,1719,1740,1763,1786,1812,1852,1918,2025,2041,2087,2106,2123,2139,2164,2182,2201],"649":[252],"|":[253,275,299,328,350,370,395,420,445,469,490,516,535,557,578,598,614,638,658,680,708,729,751,771,793,814,836,859,881,902,924,948,973,996,1017,1033,1052,1073,1093,1111,1134,1155,1173,1193,1211,1232,1254,1273,1295,1316,1333,1354,1372,1396,1416,1435,1457,1478,1502,1524,1541,1561,1582,1604,1625,1646,1664,1685,1705,1724,1745,1768,1791,1817,1838,1855,1878,1903,1923,1944,1963,1988,2008,2030,2044,2062,2090,2109,2126,2142,2167,2185,2204],"1":[254,349,444,468,489,517,556,558,577,613,639,707,728,770,772,815,837,903,923,947,972,1018,1034,1072,1112,1133,1154,1174,1194,1212,1231,1233,1253,1272,1296,1317,1334,1355,1373,1395,1397,1415,1434,1458,1479,1503,1523,1560,1562,1603,1605,1626,1647,1665,1686,1706,1723,1725,1744,1746,1769,1816,1839,1856,1879,1904,1924,1945,1964,1989,2009,2045,2061,2063,2091,2110,2127,2143,2168,2186,2205],"Sep":[255,773,838,2128,2144,2169],"2022":[256,278,302,331,353],"Cross":[257,279,303,332,354,374,399,424,449,473,494,520,539,561,582,602,618,642,662,684,712,733,755,775,797,818,840,863,885,906,928,952,977,1000,1021,1037,1056,1077,1097,1115,1138,1159,1177,1197,1215,1236,1258,1277,1299,1320,1337,1358,1376,1400,1420,1439,1461,1482,1506,1528,1545,1565,1586,1608,1629,1650,1668,1689,1709,1728,1749,1772,1842,1859,1882,1907,1927,1948,1967,1992,2012,2048,2066,2094,2113,2130,2146,2171,2189,2208],"Ref":[258,280,304,333,355,375,400,425,450,474,495,521,540,562,583,603,619,643,663,685,713,734,756,776,798,819,841,864,886,907,929,953,978,1001,1022,1038,1057,1078,1098,1116,1139,1160,1178,1198,1216,1237,1259,1278,1300,1321,1338,1359,1377,1401,1421,1440,1462,1483,1507,1529,1546,1566,1587,1609,1630,1651,1669,1690,1710,1729,1750,1773,1843,1860,1883,1908,1928,1949,1968,1993,2013,2049,2067,2095,2114,2131,2147,2172,2190,2209],"Refinement":[259],"seminorm":[261],"semi-Hilbertian":[267,1551],"space":[268],"operatorsMathematica":[269],"Slovaca,":[270,653],"72,":[272],"No.":[273,297,326,348,368,393,443,467,488,514,533,555,576,596,612,656,706,727,749,769,791,857,879,922,946,971,994,1050,1071,1091,1132,1153,1171,1230,1252,1271,1293,1314,1331,1352,1370,1394,1414,1433,1455,1476,1500,1522,1539,1559,1580,1602,1623,1644,1662,1683,1703,1722,1743,1766,1789,1815,1836,1876,1901,1921,1961,1986,2006,2028,2060],"4":[274,974,1274,1542,1581,1792],"9":[276,794,1294,1371,1477,1501,1987],"August":[277,492,883],"A":[281,475,686,979,1117,1730,2096,2115,2148],"Hilbert-Schmidt":[282],"semidefinite":[287,338,745],"related":[289,587,716,737,867,958,1285,1443,1465],"question":[292,342,384],"BourinPositivity,":[294],"26,":[296,347],"3":[298,369,515,534,860,1790,1877],"27":[300,1436],"June":[301,537,710,1526,1584],"Sharp":[305,541,1774],"Bounds":[306],"Generalized":[309],"Logarithmic":[310],"Operator":[311,315,322,439,510,529,1085,1463,1547,1576,1778],"by":[317,546],"Weighted":[318],"Ones":[319],"Classical":[321],"OnesMathematics,":[323],"10,":[325],"10":[327,329,1051,1645,1684],"May":[330,471,580,1075,1356,1418,1480,1504,2225],"Bourin":[344,386],"IIIPositivity,":[345],"23":[351,1417],"February":[352,600,998],"Unitarily":[356,2016],"meansThe":[362],"Journal":[363,388,989,1385,1781,1807,2020,2215],"Analysis,":[365,1168,1659,1833,1958,2003,2057],"29,":[367],"12":[371,792],"January":[372,518,795,926,950,1157,1275,1437,1990],"2021":[373,398,423],"semi-definite":[380],"IIInternational":[387],"Mathematics,":[390,552,609,854,991,1030,1367],"32,":[392],"07":[394],"April":[397,2223],"Extensions":[401],"arithmetic\u2013geometric":[404,435,623,693,740,821,1003,1693,1753,1912],"means":[405,760,1971],"Young's":[407,566],"accretive":[411],"applicationsLinear":[414,829,2102],"Multilinear":[416,592,787,875,1046,1327,1872,1897],"Algebra,":[417,593,788,876,1047,1328,1873,1898],"16":[419,536,579],"20":[421,659,709,1525],"March":[422,753,1054,1543],"Generalizations":[426],"version":[432],"mean":[436,545,548,624,694,741,822,1004,1103,1694,1754,1913,2078,2153,2193],"inequalityAdvances":[437],"Theory,":[440,511,530,1577],"6,":[442],"7":[446,730,1172],"October":[447,861,1095,1793],"2020":[448,472,493,519,538,560],"New":[451,1380],"proofs":[452],"two":[454],"recent":[455,870],"normsJournal":[460],"Inequalities":[462,483,571,701,722,917,941,966,1127,1148,1247,1260,1266,1409,1428,1517,1775,1861,1998,2014,2051],"2020,":[466,487],"generalized":[476],"H\u00f6lder-type":[477],"measurable":[480],"operatorsJournal":[481,939],"8":[491,882,1255,1315,1332,1583],"Positive":[496,1079,1670,1800],"definiteness":[497],"functions":[500,1283],"comparison":[502],"power":[504],"difference":[505],"meansAdvances":[508],"5,":[513,532,554,1393],"his":[525],"mathematical":[526],"achievementsAdvances":[527],"Heron":[547],"other":[550],"meansAIMS":[551],"Jan":[559,904,1019,1035,1234,1374,1398,1563,1606,1627,1840,1857,1946],"The":[563,1691],"interpolation":[564],"inequality":[567,668,695,823,985,1005,1100,1404,1695,1733,1755,1846,2079,2098,2154,2194],"using":[568,669],"dyadicsJournal":[569],"2019,":[575],"2019":[581,641],"Some":[584,1238,1279,1379,1508,1777,1884,1929],"Kwong":[589,1282],"functionsLinear":[590],"67,":[595,1090],"5":[597,750,880,1053,1353],"2018":[601,617,661,683,711,732,754,774],"Mixed":[605],"InequalitiesResults":[607,852],"74,":[611],"17":[615],"November":[616,660,731,975],"Unification":[620],"H\u00f6lder":[626,1063],"normsLinear":[631,2083],"562":[637],"Feb":[640],"Refinements":[644,1024,1140,1422],"heinz":[647],"matricesMathematica":[652],"68,":[655,1579],"Establishment":[664],"new":[667,1239],"extended":[670],"type":[672],"meanJournal":[673],"Physics:":[675],"Conference":[676],"1139":[679],"31":[681,1156,1818,2031],"December":[682],"generalization":[687,981],"an":[689,2074],"application":[690],"Frobenius":[698],"normJournal":[699],"2018,":[705,726],"meansJournal":[720,1165],"matricesPositivity,":[746],"22,":[748],"24":[752,1094],"accurate":[758,1059],"inequalitiesJournal":[761,964,1426],"Analysis":[764,1597,1784,1810,1943,2023,2218],"465,":[768],"Young":[778,849,932,1026,1589],"faithful":[783],"tracial":[784],"statesLinear":[785],"65,":[790,878],"2017":[796,817,839,905],"Contractive":[799,887,1179],"ideals":[803,891,1183],"IIILinear":[807],"530":[813],"Oct":[816,1175,1195,1318,1648],"528":[835],"Further":[842,1199],"Generalizations,":[843],"Refinements,":[844],"Reverses":[846,930,1039],"71,":[856,1070],"3-4":[858],"2016":[862,884,927,951,976,999,1020,1032,1036],"Interpolating":[865,1751],"result":[871],"AudenaertLinear":[873],"IILinear":[895],"513":[901],"Tracial":[908],"majorisation":[910],"mean-type":[912],"matricesJournal":[915,1125,1146,1224,1245,1264,1515,1594],"2016,":[921,945,970],"21":[925],"linear":[938],"29":[949],"Cauchy-Schwarz":[961,1969,2097],"operatorsInternational":[988],"27,":[993,1814],"02":[995],"25":[997],"products":[1007,1220,2072],"three":[1009],"matricesLinear":[1010,1870,1895],"488":[1016],"Multiple-Term":[1023],"Type":[1027,1382],"InequalitiesJournal":[1028],"variations":[1041],"inequalityLinear":[1044,1204,1469],"63,":[1049],"2014":[1055,1137,1158,1176,1196,1214,1235],"Young,":[1060],"Heinz,":[1061],"matricesPeriodica":[1066],"Mathematica":[1067],"Hungarica,":[1068],"2015":[1076,1096,1114],"Solutions":[1080],"Class":[1083],"EquationsUkrainian":[1086],"Journal,":[1088],"2":[1092,1456,1540,1624,1837,1902,1962,2007,2029],"Zhan's":[1099],"A\u2013G":[1102],"inequalitiesLinear":[1104,1186,1286,1325,1914,2037,2135],"470":[1110],"Apr":[1113,1213,1707,1747,1905,1965,2064,2206],"family":[1118],"refinements":[1120,1200,1240],"2014,":[1131,1152],"22":[1135],"July":[1136,1819,2032,2228],"Strong":[1161],"monotonicity":[1162],"various":[1164],"Functional":[1167,1658,1832,1957,2002,2056],"267,":[1170],"459":[1192],"447":[1210],"Trace":[1217],"Physics,":[1227],"55,":[1229],"2013,":[1251,1270],"September":[1256],"2013":[1257,1276,1298,1319,1336,1357,1375,1399],"eigenvalues":[1262],"results":[1280],"439,":[1292,1313],"Nov":[1297,1687],"value":[1303,1732],"meansLinear":[1307,1736],"Refined":[1322],"61,":[1330],"Aug":[1335],"Iterative":[1339],"learning":[1340],"control":[1341],"tracking":[1344],"problems":[1345,1886],"specified":[1347],"data":[1348],"pointsAutomatica,":[1349],"49,":[1351],"Improved":[1360,1402,1588],"via":[1363],"Jensen":[1365],"functionalOpen":[1366],"11,":[1369],"Fractional":[1381],"InequalitiesInternational":[1384],"Advanced":[1387],"Pervasive":[1388],"Ubiquitous":[1390],"Computing,":[1391],"applicationJournal":[1407],"2012,":[1413,1432],"2012":[1419,1438,1460,1481,1505],"geometric":[1447,2077],"meanLinear":[1448],"437,":[1454],"Jul":[1459,1726,2010,2092,2111],"Corach\u2013Porta\u2013Recht":[1468],"436,":[1475,1499],"some":[1485,1674,2133],"norms":[1490,1513,1868],"valuesLinear":[1493],"2011,":[1521],"2011":[1527,1544,1564],"Min":[1530],"Matrices":[1531],"MatricesThe":[1534],"Intelligencer,":[1536],"33,":[1538],"spacesLinear":[1552],"434,":[1558],"Convexity":[1569],"MeansIntegral":[1573],"Equations":[1574,1798],"2010":[1585,1607,1628],"361,":[1601],"Analysis:":[1611],"Monotone":[1613],"Functions,":[1614],"Means,":[1616],"MajorizationInterdisciplinary":[1618],"Information":[1619],"Sciences,":[1620],"16,":[1622],"Normal":[1631],"idealsLinear":[1637],"431,":[1643],"2009":[1649],"idealsJournal":[1656],"255,":[1661],"Dec":[1666],"2008":[1667,1688,1708],"solutions":[1672],"equationsLinear":[1676],"429,":[1682],"revisitedLinear":[1696],"428,":[1702],"8-9":[1704],"infinite":[1714],"divisibilityLinear":[1715],"424,":[1721],"2007":[1727,1748],"422,":[1742],"versionLinear":[1759],"413,":[1765],"2-3":[1767],"Mar":[1770,1880,1925,2187],"2006":[1771,2229],"MeansDriss":[1779],"DrissiSIAM":[1780,1806],"28,":[1788],"2006AbstractPDF":[1794,1820,2033],"(120":[1795],"KB)Generalized":[1796],"Lyapunov":[1797],"Definite":[1801],"FunctionsRajendra":[1802],"Driss":[1805],"(145":[1821],"KB)Cauchy\u2013Schwarz":[1822],"weak\u2217-integrals":[1826],"valued":[1829],"functionsJournal":[1830],"218,":[1835],"2005":[1841],"self-adjointnessLinear":[1848],"377":[1854],"2004":[1858],"hadamard":[1863,1889],"48,":[1875],"2001":[1881],"research":[1885],"47,":[1900],"2000":[1906,1926,1947],"308,":[1920],"1-3":[1922],"Comments":[1930],"Bibliography":[1933],"Frucht\u2014Kantorovich":[1936],"Wielandt":[1938],"InequalitiesInnovations":[1939],"Multivariate":[1941],"Statistical":[1942],"Comparison":[1950],"Various":[1952],"Means":[1953],"OperatorsJournal":[1955,2000],"163,":[1960],"1999":[1966],"elementary":[1974],"into":[1976],"idealsProceedings":[1978],"American":[1981],"Society,":[1983],"126,":[1985],"1998":[1991,2011],"Arithmetic\u2013Geometric":[1994],"Related":[1997],"156,":[2005],"Invariant":[2017],"NormsXingzhi":[2018],"ZhanSIAM":[2019],"20,":[2027],"(218":[2034],"KB)Geometric":[2035],"258":[2043],"Jun":[2046],"1997":[2047,2065],"Self-Adjoint":[2053],"DerivationsJournal":[2054],"145,":[2059],"arithmetic":[2075],"-":[2076],"223-224":[2089,2108],"1995":[2093,2112],"survey":[2116],"DavisLinear":[2119],"208-209":[2125,2141,2166],"1994":[2129,2145,2170,2188],"note":[2149],"arithmetic-geometric":[2152],"normLinear":[2160],"Majorizations":[2173],"199":[2184],"arithmetic-geometric-harmonic":[2192],"involving":[2195],"productsLinear":[2197],"184":[2203],"1993":[2207,2232],"Volume":[2210],"14,":[2211],"Issue":[2212],"1|":[2213],"1993SIAM":[2214],"Applications1-316":[2220],"History":[2221],"Submitted:11":[2222],"1990Accepted:09":[2224],"1991Published":[2226],"online:17":[2227],"InformationCopyright":[2230],"\u00a9":[2231],"Society":[2233],"Industrial":[2235,2256],"Applied":[2237,2258],"MathematicsKeywordsgeometric":[2238],"normMSC":[2242],"codes15A4215A6047A3047B0547B10PDF":[2243],"Download":[2244],"Article":[2245],"Publication":[2247],"DataArticle":[2248],"DOI:10.1137/0614012Article":[2249],"page":[2250],"range:pp.":[2251],"132-136ISSN":[2252],"(print):0895-4798ISSN":[2253],"(online):1095-7162Publisher:Society":[2254]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":15},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":9},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":16},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":11},{"year":2015,"cited_by_count":11},{"year":2014,"cited_by_count":12},{"year":2013,"cited_by_count":14},{"year":2012,"cited_by_count":11}],"updated_date":"2026-06-16T09:24:06.705377","created_date":"2025-10-10T00:00:00"}