Rational Criteria for Diagonalizability of Real Matrices

Abstract

The purpose of this note is to obtain rational criteria for diagonalizability of real matrices through the analysis of the moment and Gram matrices associated to a given real matrix. These concepts were introduced by Horn and Lopatin in [R.A. Horn and A.K. Lopatin. The moment and Gram matrices, distinct eigenvalues and zeroes, and rational criteria for diagonalizability. Linear Algebra and its Applications, 299:153-163, 1999] for complex matrices. However, when the matrix is real, it is possible to combine their results with the Borchardt-Jacobi Theorem, in order to get new and noteworthy rational criteria.