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A necessary and sufficient condition for simultaneous diagonalization of two hermitian matrices and its application

Published online by Cambridge University Press:  18 May 2009

Yik-Hoi Au-Yeung
Yik-Hoi Au-Yeung
Affiliation:
University of Hong Kong
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We denote by F the field R of real numbers, the field C of complex numbers, or the skew field H of real quaternions, and by Fn an n dimensional left vector space over F. If A is a matrix with elements in F, we denote by A* its conjugate transpose. In all three cases of F, an n × n matrix A is said to be hermitian if A = A*, and we say that two n × n hermitian matrices A and B with elements in F can be diagonalized simultaneously if there exists a non singular matrix U with elements in F such that UAU* and UBU* are diagonal matrices. We shall regard a vector u ∈ Fn as a l × n matrix and identify a 1 × 1 matrix with its single element, and we shall denote by diag {A1, …, Am} a diagonal block matrix with the square matrices A1, …, Am lying on its diagonal.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 11 , Issue 1 , January 1970 , pp. 81 - 83
Copyright
Copyright © Glasgow Mathematical Journal Trust 1970

References

REFERENCES

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