Some new results on the P-type properties of Z-transformations on symmetric cones
This article is on Z -transformations with respect to a symmetric cone in a Euclidean Jordan algebra. Motivated by a well known result on Z matrices (i.e. matrices with off diagonal entries are non-positive), we show that various P -type properties are equivalent for a Z -transformation. These P -ty...
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| Veröffentlicht in: | Positivity : an international journal devoted to the theory and applications of positivity in analysis 2022-11, Vol.26 (5) |
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| container_issue | 5 |
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| container_title | Positivity : an international journal devoted to the theory and applications of positivity in analysis |
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| creator | Ramamurthy, Balaji Mondal, Chiranjit |
| description | This article is on
Z
-transformations with respect to a symmetric cone in a Euclidean Jordan algebra. Motivated by a well known result on
Z
matrices (i.e. matrices with off diagonal entries are non-positive), we show that various
P
-type properties are equivalent for a
Z
-transformation. These
P
-type properties arise from the theory of linear complementarity problems. Precisely, by utilizing the concept of principal subtransformations in a Euclidean Jordan algebra, we show that for a
Z
-transformation, the so-called completely
Q
, completely
P
and positive principal minor properties are equivalent. Examples of
Z
-transformations with completely
P
-property are then given. These examples are constructed by obtaining some new results in linear complementarity problems which are of independent interest. |
| doi_str_mv | 10.1007/s11117-022-00939-5 |
| format | Article |
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Z
-transformations with respect to a symmetric cone in a Euclidean Jordan algebra. Motivated by a well known result on
Z
matrices (i.e. matrices with off diagonal entries are non-positive), we show that various
P
-type properties are equivalent for a
Z
-transformation. These
P
-type properties arise from the theory of linear complementarity problems. Precisely, by utilizing the concept of principal subtransformations in a Euclidean Jordan algebra, we show that for a
Z
-transformation, the so-called completely
Q
, completely
P
and positive principal minor properties are equivalent. Examples of
Z
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P
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Z
-transformations with respect to a symmetric cone in a Euclidean Jordan algebra. Motivated by a well known result on
Z
matrices (i.e. matrices with off diagonal entries are non-positive), we show that various
P
-type properties are equivalent for a
Z
-transformation. These
P
-type properties arise from the theory of linear complementarity problems. Precisely, by utilizing the concept of principal subtransformations in a Euclidean Jordan algebra, we show that for a
Z
-transformation, the so-called completely
Q
, completely
P
and positive principal minor properties are equivalent. Examples of
Z
-transformations with completely
P
-property are then given. These examples are constructed by obtaining some new results in linear complementarity problems which are of independent interest.</description><subject>Algebra</subject><subject>Calculus of Variations and Optimal Control; Optimization</subject><subject>Decomposition</subject><subject>Econometrics</subject><subject>Equivalence</subject><subject>Fourier Analysis</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Matrices (mathematics)</subject><subject>Operator Theory</subject><subject>Potential Theory</subject><subject>Transformations</subject><issn>1385-1292</issn><issn>1572-9281</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><sourceid>8G5</sourceid><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><sourceid>GUQSH</sourceid><sourceid>M2O</sourceid><recordid>eNpFUE1LxDAQDaLguvoHPAU8R_PRNs1RFr9gQcU9eQlpO9Uu26QmWWT_veOu4Fzmwbx58-YRcin4teBc3ySBpRmXknFulGHlEZmJUktmZC2OEau6ZEIaeUrOUlpzjmsFn5HXtzAC9fBNI6TtJicaPM2fQF9Y3k1ApxgmiHkAHPT0neXofOpDHF0egt-z024cIcehpW3wkM7JSe82CS7--pys7u9Wi0e2fH54Wtwu2YS-MnpRRiBybetqU9S8KWThukaqzhmnm74rpCibXvOaV1XfgFG66roK_6lMp9WcXB1k0eHXFlK267CNHi9aqUWlahQXyFIHVpri4D8g_rMEt7_R2UN0FqOz--hsqX4ANi5hdw</recordid><startdate>20221101</startdate><enddate>20221101</enddate><creator>Ramamurthy, Balaji</creator><creator>Mondal, Chiranjit</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>3V.</scope><scope>7WY</scope><scope>7WZ</scope><scope>7XB</scope><scope>87Z</scope><scope>88I</scope><scope>8AO</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>8FL</scope><scope>8G5</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BEZIV</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>FRNLG</scope><scope>F~G</scope><scope>GNUQQ</scope><scope>GUQSH</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K60</scope><scope>K6~</scope><scope>K7-</scope><scope>L.-</scope><scope>L6V</scope><scope>M0C</scope><scope>M2O</scope><scope>M2P</scope><scope>M7S</scope><scope>MBDVC</scope><scope>P5Z</scope><scope>P62</scope><scope>PQBIZ</scope><scope>PQBZA</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PTHSS</scope><scope>Q9U</scope></search><sort><creationdate>20221101</creationdate><title>Some new results on the P-type properties of Z-transformations on symmetric cones</title><author>Ramamurthy, Balaji ; 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Z
-transformations with respect to a symmetric cone in a Euclidean Jordan algebra. Motivated by a well known result on
Z
matrices (i.e. matrices with off diagonal entries are non-positive), we show that various
P
-type properties are equivalent for a
Z
-transformation. These
P
-type properties arise from the theory of linear complementarity problems. Precisely, by utilizing the concept of principal subtransformations in a Euclidean Jordan algebra, we show that for a
Z
-transformation, the so-called completely
Q
, completely
P
and positive principal minor properties are equivalent. Examples of
Z
-transformations with completely
P
-property are then given. These examples are constructed by obtaining some new results in linear complementarity problems which are of independent interest.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s11117-022-00939-5</doi></addata></record> |
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| identifier | ISSN: 1385-1292 |
| ispartof | Positivity : an international journal devoted to the theory and applications of positivity in analysis, 2022-11, Vol.26 (5) |
| issn | 1385-1292 1572-9281 |
| language | eng |
| recordid | cdi_proquest_journals_2716381151 |
| source | EBSCOhost Business Source Complete; Springer Nature - Complete Springer Journals |
| subjects | Algebra Calculus of Variations and Optimal Control Optimization Decomposition Econometrics Equivalence Fourier Analysis Mathematics Mathematics and Statistics Matrices (mathematics) Operator Theory Potential Theory Transformations |
| title | Some new results on the P-type properties of Z-transformations on symmetric cones |
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