Accession Number : AD0673286

Title :   CONTRIBUTION TO THE THEORY OF MATRICES PARTITIONED INTO BLOCKS.

Descriptive Note : Final technical rept. 1 Jun 67 - 15 Jun 68,

Corporate Author : BASEL UNIV (SWITZERLAND) MATHEMATICS INST

Personal Author(s) : Ostrowski,Alexander M.

Report Date : JUN 1968

Pagination or Media Count : 10

Abstract : New inequalities have been obtained for the inertia triple of certain partitioned matrices, using theorems on skew-triangular block (STB) matrices. Further properties of the Schur complement were obtained, and applications were made to matrix inequalities and computation of eigenvalues. Several results were obtained on cones of matrices and vectors, and an extension of the well-known Perron-Frobenius theorem was proved. Also a necessary and sufficient condition was derived, in order that to a given matrix corresponds a cone on which it is a positive operator. Easily computed upper and lower bounds were obtained for the maximum and minimum roots of an Hermitian matrix. (Author)

Descriptors :   (*MATRICES(MATHEMATICS), REPORTS), PERMUTATIONS, TOPOLOGY, OPERATORS(MATHEMATICS), INEQUALITIES, SWITZERLAND

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE