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On Weakly Positive Matrices

Published online by Cambridge University Press:  20 November 2018

Eugene P. Wigner
Eugene P. Wigner*
Affiliation:
Princeton University
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A matrix is said to be positive definite if it is hermitian and if all of its characteristic values are positive. It is well known, and easy to prove, that the necessary and sufficient condition for a matrix P to be positive definite is that its hermitian quadratic form

with any vector v ≠ 0 be positive. (This will imply, in the present article, that it is real.) It is easy to see from (1) that if P1 and P2 are positive definite, the same holds of a1P1 + a2P2 if a1 and a2 are positive numbers.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 15 , 1963 , pp. 313 - 317
Copyright
Copyright © Canadian Mathematical Society 1963