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Positivity of Block Tridiagonal Matrices
SIAM Journal on Matrix Analysis and Applications, 1998The authors give some results concerning the disconjugacy of linear Hamiltonian difference systems \[ \Delta x_k = A_k x_{k+1} + B_k u_k,\quad \Delta u_k = C_k x_{k+1} - A_k^T u_k \] and hence positive definiteness of the discrete quadratic functional \[ {\mathcal F}(x,u) ={\sum_{k=0}^N} \{u_k^T B_k u_k + x_{k+1}^T C_k x_{k+1}\} \] to positive ...
Bohner, Martin, Došlý, Ondřej
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1999
A Toeplitz matrix is constant along the parallels to the main diagonal. Matrices whose entries in the parallels to the main diagonal form periodic sequences (with the same period N) are referred to as block Toeplitz matrices. Equivalently, A is a block Toeplitz matrix if and only if $$ A = \left( {\begin{array}{*{20}{c}} {{a_0}}{{a_{ - 1}}}{{a_ ...
Albrecht Böttcher, Bernd Silbermann
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A Toeplitz matrix is constant along the parallels to the main diagonal. Matrices whose entries in the parallels to the main diagonal form periodic sequences (with the same period N) are referred to as block Toeplitz matrices. Equivalently, A is a block Toeplitz matrix if and only if $$ A = \left( {\begin{array}{*{20}{c}} {{a_0}}{{a_{ - 1}}}{{a_ ...
Albrecht Böttcher, Bernd Silbermann
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Linear Algebra and its Applications, 2019
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Sejong Kim, Hosoo Lee, Yongdo Lim
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sejong Kim, Hosoo Lee, Yongdo Lim
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Group invertible block matrices
Frontiers of Mathematics in China, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zheng, Baodong +2 more
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Further Block Generalizations of Nekrasov Matrices
Journal of Mathematical Sciences, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A Block Generalization of Nekrasov Matrices
Journal of Mathematical Sciences, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Linear Algebra and its Applications
The permanent of a matrix is defined similarly to the determinant, only differing in that the signatures of the permutations are not considered. Both matrix functions share common properties, but the multiplicative property of determinants does not hold for permanents. It should be stressed that the evaluation of permanents is in general very difficult.
Rodtes, Kijti, Anwar, Muhammad Fazeel
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The permanent of a matrix is defined similarly to the determinant, only differing in that the signatures of the permutations are not considered. Both matrix functions share common properties, but the multiplicative property of determinants does not hold for permanents. It should be stressed that the evaluation of permanents is in general very difficult.
Rodtes, Kijti, Anwar, Muhammad Fazeel
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Positive Definite Block Matrices
1990This chapter is a positive matrix version of Chapter IV. First we give a complete characterization of all 2 by 2 and 3 by 3 positive block matrices. Then this is used to obtain some standard results for positive Toeplitz matrices and the Levinson algorithm.
Ciprian Foias, Arthur E. Frazho
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5 Block Matrices and π -Triangular Matrices
2003The present chapter is devoted to block matrices. In particular, we derive the invertibility conditions, which supplement the generalized Hadamard criterion and some other well-known results for block matrices.
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