On a Banach's problem of infinite matrices

M. Nosarzewska

Displaying similar documents to “On a Banach's problem of infinite matrices”

Basic Properties of Determinants of Square Matrices over a Field 1

Karol Pąk (2007)

Formalized Mathematics

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In this paper I present basic properties of the determinant of square matrices over a field and selected properties of the sign of a permutation. First, I define the sign of a permutation by the requirement [...] where p is any fixed permutation of a set with n elements. I prove that the sign of a product of two permutations is the same as the product of their signs and show the relation between signs and parity of permutations. Then I consider the determinant of a linear combination...

On the Permanent of a Matrix

Ewa Romanowicz, Adam Grabowski (2006)

Formalized Mathematics

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We introduce the notion of a permanent [13] of a square matrix. It is a notion somewhat related to a determinant, so we follow closely the approach and theorems already introduced in the Mizar Mathematical Library for the determinant. Unfortunately, the formalization of the latter notion is at its early stage, so we had to prove many very elementary auxiliary facts.

On certain generalized circulant matrices.

Dedó, E., Marini, A., Salvi, N.Z. (2003)

Mathematica Pannonica

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A nested multiplicative commutator equation

Beitia, Maria Asunción, Cain, Bryan E., Zaballa, Ion (1988)

Portugaliae mathematica

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Pattern avoidance in matrices.

Kitaev, Sergey, Mansour, Toufik, Vella, Antoine (2005)

Journal of Integer Sequences [electronic only]

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Permutation matrices and matrix equivalence over a finite field.

Mullen, Gary L. (1981)

International Journal of Mathematics and Mathematical Sciences

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Generalizations of Nekrasov matrices and applications

Ljiljana Cvetković, Vladimir Kostić, Maja Nedović (2015)

Open Mathematics

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In this paper we present a nonsingularity result which is a generalization of Nekrasov property by using two different permutations of the index set. The main motivation comes from the following observation: matrices that are Nekrasov matrices up to the same permutations of rows and columns, are nonsingular. But, testing all the permutations of the index set for the given matrix is too expensive. So, in some cases, our new nonsingularity criterion allows us to use the results already...

Aztec diamonds and Baxter permutations.

Canary, Hal (2010)

The Electronic Journal of Combinatorics [electronic only]

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When does the inverse have the same sign pattern as the transpose?

Carolyn A. Eschenbach, Frank J. Hall, Deborah L. Harrell, Zhongshan Li (1999)

Czechoslovak Mathematical Journal

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By a sign pattern (matrix) we mean an array whose entries are from the set ${+, -, 0}$ . The sign patterns $A$ for which every real matrix with sign pattern $A$ has the property that its inverse has sign pattern $A^{T}$ are characterized. Sign patterns $A$ for which some real matrix with sign pattern $A$ has that property are investigated. Some fundamental results as well as constructions concerning such sign pattern matrices are provided. The relation between these sign patterns and the sign patterns of orthogonal...