Simultaneous Diagonalization and SVD of Commuting Matrices
Ronald P. Nordgren
TL;DR
This paper introduces a method for simultaneous diagonalization and SVD of commuting matrices, extending existing techniques to matrices with multiple eigenvalues and analyzing permutation effects.
Contribution
It provides a matrix-based approach for simultaneous diagonalization and SVD of commuting matrices, including cases with repeated eigenvalues, and examines permutation impacts.
Findings
Method enables simultaneous diagonalization of commuting matrices with multiple eigenvalues.
SVD of certain classes of commuting matrices is achieved.
Permutation effects on matrix decompositions are analyzed.
Abstract
We present a matrix version of a known method of constructing common eigenvectors of two diagonalizable commuting matrices, thus enabling their simultaneous diagonalization. The matrices may have simple eigenvalues of multiplicity greater than one. The singular value decomposition (SVD) of a class of commuting matrices also is treated. The effect of row/column permutation is examined. Examples are given.
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Taxonomy
TopicsMatrix Theory and Algorithms · graph theory and CDMA systems