Displaying similar documents to “An inequality for determinants with real entries”

Properties of the determinant of a rectangular matrix

Anna Makarewicz, Piotr Pikuta, Dominik Szałkowski (2014)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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In this paper we present new identities for the Radić’s determinant of a rectangular matrix. The results include representations of the determinant of a rectangular matrix as a sum of determinants of square matrices and description how the determinant is affected by operations on columns such as interchanging columns, reversing columns or decomposing a single column.

Some new formulas for π .

Almkvist, Gert, Krattenthaler, Christian, Petersson, Joakim (2003)

Experimental Mathematics

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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...

Companion matrices and their relations to Toeplitz and Hankel matrices

Yousong Luo, Robin Hill (2015)

Special Matrices

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In this paper we describe some properties of companion matrices and demonstrate some special patterns that arisewhen a Toeplitz or a Hankel matrix is multiplied by a related companion matrix.We present a necessary and sufficient condition, generalizing known results, for a matrix to be the transforming matrix for a similarity between a pair of companion matrices. A special case of our main result shows that a Toeplitz or a Hankel matrix can be extended using associated companion matrices,...