论文信息 - Perron-Frobenius properties of Ax − λBx - 字舞流文

Perron-Frobenius properties of Ax − λBx

Abstract The purpose of this work is to extend some of the results of Perron and Frobenius to the following generalized eigenvalue problems: Ax = λBx and A ′ y = λB ' y , where A and B are m × n real matrices and the prime denotes the transpose.

Olvi L. Mangasarian | O. Mangasarian

[1] A. J. Goldman,et al. Polyhedral Convex Cones , 1956 .

[2] Olvi L. Mangasarian,et al. Nonlinear Programming , 1969 .

[3] Th. Motzkin. Beiträge zur Theorie der linearen Ungleichungen , 1936 .

[4] David Gale. The theory of linear economic models , 1960 .

[5] George B. Dantzig,et al. Linear programming and extensions , 1965 .

[6] Ivan Erdelyi,et al. On the matrix equation Ax = λBx , 1967 .

[7] J. Gillis,et al. Matrix Iterative Analysis , 1961 .

[8] T. Motzkin. Two Consequences of the Transposition Theorem on Linear Inequalities , 1951 .

[9] R. Bellman,et al. A Survey of Matrix Theory and Matrix Inequalities , 1965 .

[10] M. Kreĭn,et al. Linear operators leaving invariant a cone in a Banach space , 1950 .

[11] M. Slater,et al. A Note on Motzkin's Transposition Theorem , 1951 .