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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Walter Philipp (1964)
Compositio Mathematica
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David M. Arnold, Adolf Mader, Otto Mutzbauer, Ebru Solak (2013)
Czechoslovak Mathematical Journal
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Almost completely decomposable groups with a critical typeset of type and a -primary regulator quotient are studied. It is shown that there are, depending on the exponent of the regulator quotient , either no indecomposables if ; only six near isomorphism types of indecomposables if ; and indecomposables of arbitrary large rank if .
Sivasubramanian, Sivaramakrishnan (2010)
The Electronic Journal of Combinatorics [electronic only]
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Almkvist, Gert, Krattenthaler, Christian, Petersson, Joakim (2003)
Experimental Mathematics
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Weining Chen, Guixin Deng, Huadong Su (2020)
Czechoslovak Mathematical Journal
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We investigate the formal matrix ring over defined by a certain system of factors. We give a method for constructing formal matrix rings from non-negative integer matrices. We also show that the principal factor matrix of a binary system of factors determine the structure of the system.
Johnson, Charles R., Merris, Russell, Pierce, Stephen (1985-1986)
Portugaliae mathematica
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Anna Makarewicz, Piotr Pikuta, Dominik Szałkowski (2014)
Annales UMCS, 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
Changjiang Bu, Wenzhe Wang, Jiang Zhou, Lizhu Sun (2014)
Czechoslovak Mathematical Journal
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The sign pattern of a real matrix , denoted by , is the -matrix obtained from by replacing each entry by its sign. Let denote the set of all real matrices such that . For a square real matrix , the Drazin inverse of is the unique real matrix such that , and , where is the Drazin index of . We say that has signed Drazin inverse if for any , where denotes the Drazin inverse of . In this paper, we give necessary conditions for some block triangular matrices...