Linear maps that preserve matrices annihilated by a polynomial
نویسندگان
چکیده
منابع مشابه
Multiplicative maps on invertible matrices that preserve matricial properties
Descriptions are given of multiplicative maps on complex and real matrices that leave invariant a certain function, property, or set of matrices: norms, spectrum, spectral radius, elementary symmetric functions of eigenvalues, certain functions of singular values, (p, q) numerical ranges and radii, sets of unitary, normal, or Hermitian matrices, as well as sets of Hermitian matrices with fixed ...
متن کاملEla Multiplicative Maps on Invertible Matrices That Preserve Matricial Properties
Descriptions are given of multiplicative maps on complex and real matrices that leave invariant a certain function, property, or set of matrices: norms, spectrum, spectral radius, elementary symmetric functions of eigenvalues, certain functions of singular values, (p, q) numerical ranges and radii, sets of unitary, normal, or Hermitian matrices, as well as sets of Hermitian matrices with fixed ...
متن کاملLinear Operators That Preserve Graphical Properties of Matrices: Isolation Numbers
Let A be a Boolean {0, 1} matrix. The isolation number of A is the maximum number of ones in A such that no two are in any row or any column (that is they are independent), and no two are in a 2 × 2 submatrix of all ones. The isolation number of A is a lower bound on the Boolean rank of A. A linear operator on the set of m× n Boolean matrices is a mapping which is additive and maps the zero mat...
متن کاملLinear operators that strongly preserve graphical properties of matrices - II
Beasley, L.B. and N.J. Pullman, Linear operators that strongly preserve graphical properties of matrices, Discrete Mathematics 104 (1992) 143-157. An operator on the set Ju of n X n matrices strongly preserves a subset 9 if it maps 9 into 9 and A\% into A\%. The operator semigroup of 9 is the semigroup of linear operators strongly preserving 9. We show that all the n x n matrix-families which a...
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An n× n fuzzy matrix A is called regular if there is an n× n fuzzy matrix G such that AGA = A. We study the problem of characterizing those linear operators T on the fuzzy matrices such that T (X) is regular if and only if X is. Consequently, we obtain that T strongly preserves regularity of fuzzy matrices if and only if there are permutation matrices P and Q such that it has the form T (X) = P...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1980
ISSN: 0024-3795
DOI: 10.1016/0024-3795(80)90192-5