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Simultaneous block triangularization and block diagonalization of sets of matrices

Authors
Journal
Linear Algebra and its Applications
0024-3795
Publisher
Elsevier
Publication Date
Volume
25
Identifiers
DOI: 10.1016/0024-3795(79)90012-0
Disciplines
  • Mathematics

Abstract

Abstract We consider the problem of simultaneously putting a set of square matrices into the same block upper triangular form with a similarity transformation, and obtain a result linking the size of the largest block to polynomial identities. This is used to yield a new proof of a theorem of Watters [20] which gives a necessary and sufficient condition for a set of matrices to be simultaneously, unitarily similar to block diagonal matrices with blocks of sizes one or two.

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