Abstract
SynopsisIn this paper are considered certain numbers called moduli associated with a rectangular matrix with complex elements. These moduli have to satisfy a set of conditions analogous to those satisfied by the modulus of a complex number. For a complex rectangular matrix A = (aij) it is shown that R(A), C(A) and | A |° are moduli of A where:where cmin(H) and cmax(H) denote, respectively, the minimum and maximum characteristic values of the hermitian matrix H, A* being the transpose conjugate of A. Using the various properties of a modulus of a matrix and taking R(A), C(A) and | A |° as the moduli, a number of known results about the characteristic values of a matrix are obtained and extended. Relations between |A|°, |A |° R(A), p(A) and C(A), ɣ(A) are also studied. These relations provide a number of results about estimates of bounds of characteristic values of sums and products of matrices.
Publisher
Cambridge University Press (CUP)
Reference12 articles.
1. “Numerical inverting of matrices”;Neumann;Bull. Amer. Math. Soc.,1947
2. A Note on Quasi-Idempotent Matrices
3. The characteristic roots of a matrix
4. A useful theorem in matrix theory
5. “Remark on Roy's paper …”;Nagy;Proc. Amer. Math. Soc.,1956