CONTRIBUTION TO THE THEORY OF MATRICES PARTITIONED INTO BLOCKS.
Final technical rept. 1 Jun 67 - 15 Jun 68,
BASEL UNIV (SWITZERLAND) MATHEMATICS INST
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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
- Theoretical Mathematics