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.

中文翻译：

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有限块-托普利茨三对角矩阵特征值的改进公式

摘要 经过简短的概述后，对具有 (K × K) 矩阵项的 (N × N) 块托普利茨三对角 (block-TT) 矩阵的特征值提出了改进（基于 Kronecker 乘积），这在应用中很常见。指出了 Toeplitz-三对角矩阵的谱特性的一些扩展。研究了可对角化对称和斜对称块TT矩阵的特征值。此外，如果某个矩阵平方根是明确定义的，则证明每个具有交换矩阵项的块-TT矩阵与相关的对称块-TT矩阵是等谱的。还实现了对用于 PDE 解的分层 Hermitian 块 TT 矩阵的特征值的进一步了解。