Bibliographic Details
| Title: |
Simultaneous block diagonalization of symmetric matrices via congruence. |
| Authors: |
Fang, Lishan1 (AUTHOR), Huang, Hua-Lin1 (AUTHOR) hualin.huang@hqu.edu.cn, Huang, Jiayan1 (AUTHOR) |
| Source: |
Linear Algebra & its Applications. May2026, Vol. 737, p193-212. 20p. |
| Subjects: |
Symmetric matrices, Matrix decomposition, Mathematical equivalence, Idempotents, Normal forms (Mathematics), Matrices (Mathematics) |
| Abstract: |
This article studies canonical forms derived from the finest simultaneous block diagonalization of a set of symmetric matrices via congruence. Our technique relies on the center theory of a set of multivariate polynomials, which we adapt for a set of symmetric matrices. We establish a bijective relationship between the simultaneous block diagonalizations of these matrices via congruence and complete sets of orthogonal idempotents of their centers. Based on this framework, we provide an algorithm relying primarily on standard linear algebra tasks. We also extend this technique to the simultaneous block diagonalizations of a set of Hermitian matrices via ⁎-congruence. In addition, we investigate the simultaneous orthogonal block diagonalizations for real matrices and the simultaneous unitary block diagonalizations for Hermitian matrices. Several examples are provided to demonstrate its effectiveness. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
