Abstract
Abstract After a short overview, improvements (based on the Kronecker product) are proposed for the eigenvalues of (N × N) block-Toeplitz tridiagonal (block-TT) matrices with (K × K) matrix-entries, common in applications. Some extensions of the spectral properties of the Toeplitz-tridiagonal matrices are pointed-out. The eigenvalues of diagonalizable symmetric and skew-symmetric block-TT matrices are studied. Besides, if certain matrix square-root is well-defined, it is proved that every block-TT matrix with commuting matrix-entries is isospectral to a related symmetric block-TT one. Further insight about the eigenvalues of hierarchical Hermitian block-TT matrices, of use in the solution of PDEs, is also achieved.
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