Computing the determinants by reducing the orders by four.
Gjonbalaj, Qefsere, Salihu, Armend (2010)
Applied Mathematics E-Notes [electronic only]
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Gjonbalaj, Qefsere, Salihu, Armend (2010)
Applied Mathematics E-Notes [electronic only]
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Benjamin, Arthur T., Shattuck, Mark A. (2007)
Integers
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Tamm, Ulrich (2001)
The Electronic Journal of Combinatorics [electronic only]
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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.
Almkvist, Gert, Krattenthaler, Christian, Petersson, Joakim (2003)
Experimental Mathematics
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Kalkbrener, M. (1997)
Mathematica Pannonica
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Li, Hsuan-Chu, Chen, Young-Ming, Tan, Eng-Tjioe (2009)
Integers
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Woan, Wen-Jin (2001)
Journal of Integer Sequences [electronic only]
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Richardson, Thomas M. (2008)
Integers
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Kitaev, Sergey, Mansour, Toufik, Vella, Antoine (2005)
Journal of Integer Sequences [electronic only]
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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...
Fallat, Shaun M., Johnson, Charles R., Smith, Ronald L. (2000)
ELA. The Electronic Journal of Linear Algebra [electronic only]
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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,...
Lee, Gwang-Yeon, Shader, Bryan L. (1998)
ELA. The Electronic Journal of Linear Algebra [electronic only]
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