Open AccessRational Criteria for Diagonalizability of Real Matrices
Author(s) -
João Ferreira Alves
Publication year - 2020
Publication title -
the electronic journal of linear algebra
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.447
H-Index - 31
eISSN - 1537-9582
pISSN - 1081-3810
DOI - 10.13001/ela.2020.5373
Subject(s) - mathematics , eigenvalues and eigenvectors , algebra over a field , moment (physics) , matrix (chemical analysis) , complex matrix , linear algebra , pure mathematics , order (exchange) , geometry , chemistry , physics , materials science , finance , classical mechanics , quantum mechanics , chromatography , economics , composite material
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.