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A Note on Non-Negative Matrices

Published online by Cambridge University Press:  20 November 2018

C. R. Putnam
C. R. Putnam*
Affiliation:
Purdue University
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This note can be regarded as an addendum to the paper (4). On the complex Hilbert space of vectors x = (x1, x2, … ,) a matrix A is said to be bounded if there exists a constant M such that ||Ax|| ≦ M||x|| whenever ||x||2 = Σ|xk|2 < ∞ ; the least such M is denoted by ||A||. Only bounded matrices A and vectors x satisfying ||x|| < ∞ will be considered in the sequel. The spectrum of A, denoted by sp(A), is the set of values for which the resolvent R(λ) = (A — λI)-1 fails to be bounded. The notation A ≥ 0 or A > 0, where A = (aij), means that, for all i and j , aij ≥ 0 or aij 0 respectively.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 13 , 1961 , pp. 59 - 62
Copyright
Copyright © Canadian Mathematical Society 1961

References

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