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A Note on a Matrix Result of Ryser

Published online by Cambridge University Press:  20 November 2018

I. S. Murphy
I. S. Murphy*
Affiliation:
University of Glasgow, Scotland
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Extract

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The purpose of this note is to give a short proof of a generalisation of a theorem of Ryser, Theorem 10.2.3 of [1], concerning matrices that occur in the theory of symmetric block designs.

The two main results of matrix theory required in the proof given below are:

  1. (1) If B, C are square matrices such that BC = zI where z is a non-zero complex number, then CB = zI

  2. (2) A matrix S which is both symmetric (i.e. S' = S) and skew-symmetric (i.e. S' = —S)is zero.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 18 , Issue 1 , April 1975 , pp. 149 - 150
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Hall, M., Combinatorial Theory (Blaisdell), 1967.Google Scholar