Some comments on \(k\)-tridiagonal matrices: determinant, spectra, and inversion

DOI10.1016/j.amc.2015.08.088zbMath1410.15053OpenAlexW1408749474MaRDI QIDQ670822

Fatih Yilmaz, Carlos Martins de Fonseca

Publication date: 20 March 2019

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2015.08.088

zbMATH Keywords

eigenvaluesdeterminantsinverse\(k\)-tridiagonal matrices

Mathematics Subject Classification ID

Eigenvalues, singular values, and eigenvectors (15A18) Toeplitz, Cauchy, and related matrices (15B05)

Related Items (17)

On some quasi anti-tridiagonal matrices ⋮ Analytic determinants and inverses of Toeplitz and Hankel tridiagonal matrices with perturbed columns ⋮ The inverses and eigenpairs of tridiagonal Toeplitz matrices with perturbed rows ⋮ Eigenpairs of a family of tridiagonal matrices: three decades later ⋮ A tridiagonalization-based numerical algorithm for computing the inverses of \((p, q)\)-pentadiagonal matrices ⋮ Tridiagonal maximum-entropy sampling and tridiagonal masks ⋮ Explicit formula for positive integer powers of \(k\)-tridiagonal Toeplitz matrices ⋮ Eigenpairs of some imperfect pentadiagonal Toeplitz matrices ⋮ A fast and reliable numerical solver for general bordered \(k\)-tridiagonal matrix linear equations ⋮ A reducing approach for symmetrically sparse banded and anti-banded matrices ⋮ On singular values related to DAEs in Kronecker canonical form ⋮ Eigenvalues and eigenvectors of tau matrices with applications to Markov processes and economics ⋮ INVERSES AND EIGENPAIRS OF TRIDIAGONAL TOEPLITZ MATRIX WITH OPPOSITE-BORDERED ROWS ⋮ Explicit determinants, inverses and eigenvalues of four band Toeplitz matrices with perturbed rows ⋮ Some determinantal considerations for pentadiagonal matrices ⋮ A periodic determinantal property for (0,1) double banded matrices ⋮ Determinants of some pentadiagonal matrices

Cites Work

• The eigenvalues of a family of persymmetric anti-tridiagonal 2-Hankel matrices
• Inversion of \(k\)-tridiagonal matrices with Toeplitz structure
• Fast block diagonalization of \(k\)-tridiagonal matrices
• An explicit formula for the determinant of a skew-symmetric pentadiagonal Toeplitz matrix
• On the eigenvalues of double band matrices
• A computational algorithm for special \(n\)th-order pentadiagonal Toeplitz determinants
• Inversion of tridiagonal matrices
• Eigenvalues and eigenvectors of some tridiagonal matrices
• Inversion of a tridiagonal Jacobi matrix
• Explicit inverse of a tridiagonal \(k\)-Toeplitz matrix
• On the zeros of complex Van Vleck polynomials
• On a constant-diagonals matrix
• On computing the determinants and inverses of some special type of tridiagonal and constant-diagonals matrices
• On the characteristic polynomial, eigenvectors and determinant of a pentadiagonal matrix
• THE LU FACTORIZATIONS AND DETERMINANTS OF THE K-TRIDIAGONAL MATRICES
• Explicit inverses of some tridiagonal matrices
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