Basic Properties of Determinants of Square Matrices over a Field
      1

Karol Pąk

Displaying similar documents to “ Basic Properties of Determinants of Square Matrices over a Field 1 ”

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 a Banach's problem of infinite matrices

M. Nosarzewska (1951)

Colloquium Mathematicae

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Determinant of Some Matrices of Field Elements

Yatsuka Nakamura (2006)

Formalized Mathematics

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Here, we present determinants of some square matrices of field elements. First, the determinat of 2 * 2 matrix is shown. Secondly, the determinants of zero matrix and unit matrix are shown, which are equal to 0 in the field and 1 in the field respectively. Thirdly, the determinant of diagonal matrix is shown, which is a product of all diagonal elements of the matrix. At the end, we prove that the determinant of a matrix is the same as the determinant of its transpose.

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...