Article ID Journal Published Year Pages File Type
4602991 Linear Algebra and its Applications 2006 4 Pages PDF
Abstract

For any n × n complex matrix A and any integer k ⩾ 1, we prove that the span of image of the map x ↦ (Ax)(k) is equal to the range of (AA∗)(k), where X∗ and X(k) denote the conjugate transpose and the kth Hadamard power of a matrix X, respectively. This settles a conjecture, due to Gorni and Tutaj-Gasińska, related to the study of the Jacobian Conjecture.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory