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Maximum Principles in matrix theory

Published online by Cambridge University Press:  18 May 2009

L. Mirsky
L. Mirsky
Affiliation:
The University Sheffield
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Unless the contrary is stated, all matrices are understood to be complex and of type n × n. The transposed conjugate of A is denoted by A*. The non-negative square roots of the characteristic roots of A*A are called the singular values of A; they will be denoted by st(A), i = 1, …, n, where s1(A)≥…≥ sn(A). The symbol [A]k denotes the k × k submatrix standing in the upper left-hand corner of A. We shall write Ei(z1, …, zn) for the j-th elementary symmetric function of z1..., zn, and E1(A) for the j-th elementary symmetric function of the characteristic roots of A. It is understood that, throughout, 1≥j≥k≥n.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 4 , Issue 1 , December 1958 , pp. 34 - 37
Copyright
Copyright © Glasgow Mathematical Journal Trust 1958

References

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