No CrossRef data available.
Article contents
A Note on Non-Negative Matrices
Published online by Cambridge University Press: 20 November 2018
Extract
Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
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
- Copyright
- Copyright © Canadian Mathematical Society 1961
References
1.
Birkhoff, G. and Varga, R. S., Reactor criticality and nonnegative matrices, J. Soc. Indust. Appl. Math., 6 (1958), 354–377.Google Scholar
2.
Herstein, I. N., A note on primitive matrices, Amer. Math. Monthly, 61 (1954), 18–20.Google Scholar
3.
Krein, M. G. and Rutman, M. A., Linear operators leaving invariant a cone in a Banach space, Uspehi Matem., Nauk (N.S.), 3 (23) 1948), 3–95; Amer. Math. Soc. Translation No. 26 (page reference in paper refers to this translation).Google Scholar
4.
Putnam, C. R., On bounded matrices with non-negative elements, Can. J. Math., 10 (1958), 587–591.Google Scholar
You have
Access