On a definition and notation of matrices. On a kind of switch matrices
Đ. Kurepa (1952)
Matematički Vesnik
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Đ. Kurepa (1952)
Matematički Vesnik
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Paulus Gerdes (2002)
Visual Mathematics
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Paulus Gerdes (2002)
Visual Mathematics
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Paulus Gerdes (2002)
Visual Mathematics
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Brydon Eastman, Kevin N. Vander Meulen (2016)
Special Matrices
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The class of sparse companion matrices was recently characterized in terms of unit Hessenberg matrices. We determine which sparse companion matrices have the lowest bandwidth, that is, we characterize which sparse companion matrices are permutationally similar to a pentadiagonal matrix and describe how to find the permutation involved. In the process, we determine which of the Fiedler companion matrices are permutationally similar to a pentadiagonal matrix. We also describe how to find...
Luis Verde-Star (2015)
Special Matrices
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We use elementary triangular matrices to obtain some factorization, multiplication, and inversion properties of triangular matrices. We also obtain explicit expressions for the inverses of strict k-Hessenberg matrices and banded matrices. Our results can be extended to the cases of block triangular and block Hessenberg matrices. An n × n lower triangular matrix is called elementary if it is of the form I + C, where I is the identity matrix and C is lower triangular and has all of its...
H. Minc (1963)
Applicationes Mathematicae
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S. Kouachi (2008)
Applicationes Mathematicae
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We give explicit expressions for the eigenvalues and eigenvectors of some tridiagonal matrices with non-constant diagonal entries. Our techniques are based on the theory of recurrent sequences.
Thomas A. Brown, Joel H. Spencer (1971)
Colloquium Mathematicae
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Carolina Blasio, João Marcos, Heinrich Wansing (2017)
Bulletin of the Section of Logic
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Starting from the notions of q-entailment and p-entailment, a two-dimensional notion of entailment is developed with respect to certain generalized q-matrices referred to as B-matrices. After showing that every purely monotonic singleconclusion consequence relation is characterized by a class of B-matrices with respect to q-entailment as well as with respect to p-entailment, it is observed that, as a result, every such consequence relation has an inferentially four-valued characterization....
Michael Cox, Kevin N. Vander Meulen, Adam Van Tuyl, Joseph Voskamp (2024)
Czechoslovak Mathematical Journal
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The Fiedler matrices are a large class of companion matrices that include the well-known Frobenius companion matrix. The Fiedler matrices are part of a larger class of companion matrices that can be characterized by a Hessenberg form. We demonstrate that the Hessenberg form of the Fiedler companion matrices provides a straight-forward way to compare the condition numbers of these matrices. We also show that there are other companion matrices which can provide a much smaller condition...
Cheng-yi Zhang, Zichen Xue, Shuanghua Luo (2016)
Open Mathematics
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It is well known that SOR iterative methods are convergent for linear systems, whose coefficient matrices are strictly or irreducibly diagonally dominant matrices and strong H-matrices (whose comparison matrices are nonsingular M-matrices). However, the same can not be true in case of those iterative methods for linear systems with weak H-matrices (whose comparison matrices are singular M-matrices). This paper proposes some necessary and sufficient conditions such that SOR iterative...
Luis Verde-Star (2017)
Special Matrices
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We show that an infinite lower Hessenberg matrix generates polynomial sequences that correspond to the rows of infinite lower triangular invertible matrices. Orthogonal polynomial sequences are obtained when the Hessenberg matrix is tridiagonal. We study properties of the polynomial sequences and their corresponding matrices which are related to recurrence relations, companion matrices, matrix similarity, construction algorithms, and generating functions. When the Hessenberg matrix is...