MATRIX FUNCTIONS PRESERVING SETS OF GENERALIZED NONNEGATIVE MATRICES

作者：Elhashash Abed^*; Szyld Daniel B

来源：Electronic Journal of Linear Algebra, 2010, 20: 673-690.

• Matrix functions
• Generalization of nonnegative matrices
• Eventually nonnegative matrices
• Eventually positive matrices
• Exponentially nonnegative matrices
• Eventually exponentially nonnegative matrices
• Perron-Frobenius property
• Strong Perron-Frobenius property

Matrix functions preserving several sets of generalized nonnegative matrices are characterized. These sets include PFn, the set of n x n real eventually positive matrices; and WPFn, the set of matrices A is an element of R-nxn such that A and its transpose have the Perron-Frobenius property. Necessary conditions and sufficient conditions for a matrix function to preserve the set of n x n real eventually nonnegative matrices and the set of n x n real exponentially nonnegative matrices are also presented. In particular, it is shown that if f(0) not equal 0 and f'(0) not equal 0 for some entire function f, then such an entire function does not preserve the set of n x n real eventually nonnegative matrices. It is also shown that the only complex polynomials that preserve the set of n x n real exponentially nonnegative matrices are p(z) = az + b, where a, b is an element of R and a >= 0.

• 出版日期2010-11