RT info:eu-repo/semantics/article
T1 Square matrices with the inverse diagonal property
A1 Furtado, Susana
A1 Johnson, Charles R.
A1 Marijuán, Carlos
A1 Pisonero, Miriam
K1 Diagonal entries
K1 Inverse
K1 M-matrix
K1 Positive definite
K1 Principal minors
K1 Totally Positive
K1 Triangular
K1 Tridiagonal
AB We identify the class of real square invertible matrices A for which the signs of the diagonal entries of A 1 match those of A, and begin their study. We say such matrices have the inverse diagonal property (IDP). This class includes many important classes: the positive definite matrices, the M-matrices, the totally positive matrices and some variants, the P-matrices, the diagonally dominant and H-matrices and their inverse classes, as well as triangular matrices. This class is closed under any real invertible diagonal multiplication on either the right or the left. So questions about this class can be reduced to the case of positive diagonal entries. Other basic properties are given. One theme is what conditions need be added to the IDP to insure membership in a familiar class. For example, the positive definite matrices are characterized as certain IDP matrices with special conditions on certain particular principal minors. The tridiagonal case is highlighted. Certain specially simple conditions on such matrices are mentioned that ensure them to be P-matrices, positive definite matrices or M-matrices. We also note that recent results about the invertibility of weakly diagonally dominant matrices are used. Examples are given throughout the paper.
PB Elsevier
SN 2307-4108 (Print)  2307-4116 (Online)
YR 2023
FD 2023
LK https://uvadoc.uva.es/handle/10324/65405
UL https://uvadoc.uva.es/handle/10324/65405
LA eng
NO Kuwait Journal of Science
NO Producción Científica
DS UVaDOC
RD 08-ago-2024