| dc.creator | JOSE ANTONIO DIAZ GARCIA | |
| dc.date | 2004-07-05 | |
| dc.date.accessioned | 2023-07-21T15:46:16Z | |
| dc.date.available | 2023-07-21T15:46:16Z | |
| dc.identifier | http://cimat.repositorioinstitucional.mx/jspui/handle/1008/684 | |
| dc.identifier.uri | https://repositorioslatinoamericanos.uchile.cl/handle/2250/7729229 | |
| dc.description | By using the linear structure theory of Magnus (12), this work proposes an alter-
native way to James (11) for obtaining the Laplace-Beltrami operator, who has the
zonal polynomials of positive definite matrix argument as eigenfunctions, in partic-
ular, an explicit expression for the matrix G(v(X)), which appears in the metric
differential form (ds)2=dv0(X)G(v(X))dv (X), is obtained; also, the invariance
f (ds)2 under congruence transformations is proved. Explicit forms for (ds)2 and G(v(X)) are also shown under the spectral decomposition X=HY H0.
In a newapproach -apart from the classical theory of James (11)- a differential metric de-
pending on the Moore-Penrose inverse is proposed for the space of m£m positive
semidefinite matrices. As in the definite case, the Laplace-Beltrami operator for
the calculation of zonal polynomials of positive semidefinite matrix argument is de-
rived. In a parallel way the invariance of (ds)2 is shown and explicit expressions
for the metric and the matrixG (¢) are obtained in terms of X and its spectral decomposition. Finally, an efficient computational method for calculating the zonal polynomials of positive semidefinite matrices are preseted. | |
| dc.format | application/pdf | |
| dc.language | eng | |
| dc.publisher | Centro de Investigación en Matemáticas AC | |
| dc.rights | info:eu-repo/semantics/openAccess | |
| dc.rights | http://creativecommons.org/licenses/by-nc/4.0 | |
| dc.subject | info:eu-repo/classification/MSC/Análisis Multivariado | |
| dc.subject | info:eu-repo/classification/cti/1 | |
| dc.subject | info:eu-repo/classification/cti/12 | |
| dc.subject | info:eu-repo/classification/cti/1209 | |
| dc.subject | info:eu-repo/classification/cti/120909 | |
| dc.subject | info:eu-repo/classification/cti/120909 | |
| dc.title | Zonal Polynomials of Positive Semidefinitive Matrix Argument | |
| dc.type | info:eu-repo/semantics/report | |
| dc.type | info:eu-repo/semantics/publishedVersion | |
| dc.audience | researchers | |
