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Unitary Transformations

Published online by Cambridge University Press:  20 November 2018

B. E. Mitchell
B. E. Mitchell*
Affiliation:
Louisiana State University
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We consider the problem of finding a unique canonical form for complex matrices under unitary transformation, the analogue of the Jordan form (1, p. 305, §3), and of determining the transforming unitary matrix (1, p. 298, 1. 2). The term “canonical form” appears in the literature with different meanings. It might mean merely a general pattern as a triangular form (the Jacobi canonical form (8, p. 64)). Again it might mean a certain matrix which can be obtained from a given matrix only by following a specific set of instructions (1). More generally, and this is the sense in which we take it, it might mean a form that can actually be described, which is independent of the method used to obtain it, and with the property that any two matrices in this form which are unitarily equivalent are identical.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 6 , 1954 , pp. 69 - 72
Copyright
Copyright © Canadian Mathematical Society 1954

References

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