Matrix Roots of Eventually Positive Matrices

Abstract

Eventually positive matrices are real matrices whose powers become and remain strictly positive. As such, eventually positive matrices are a fortiori matrix roots of positive matrices, which motivates us to study the matrix roots of primitive matrices. Using classical matrix function theory and Perron-Frobenius theory, we characterize, classify, and describe in terms of the real Jordan canonical form the $p$th-roots of eventually positive matrices.

Accepted for publication in Linear Algebra and its Applications

Cited by in corpus (4)

• Matrix roots of imprimitive irreducible nonnegative matrices
• Jordan chains of $h$-cyclic matrices
• Eventual cone invariance revisited
• On the matrix $pth$ root functions and generalized Fibonacci sequences