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On the Equivalence of Two Singular Matrix Pencils

Published online by Cambridge University Press:  20 January 2009

J. Williamson
J. Williamson
Affiliation:
The Johns Hopkins University.
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In a recent paper Turnbull, discussing a rational method for the reduction of a singular matrix pencil to canonical form, has shown how the lowest row, or column, minimal index may be determined directly without reducing the pencil to canonical form. It is the purpose of this note to show how all such indices may be determined, and at the same time to give conditions, somewhat simpler than the usual ones, for the equivalence of two matrix pencils.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 4 , Issue 4 , April 1936 , pp. 224 - 231
Copyright
Copyright © Edinburgh Mathematical Society 1936

References

page 224 note 1 Turnbull, H. W., “On the reduction of singular matrix pencils,” Proc. Edin. Math. Soc., 4 (1935), 67.CrossRefGoogle Scholar

page 224 note 2 Turnbull, & Aitken, , Canonical Matrices, p. 23.Google Scholar

page 231 note 1 Turnbull, and Aitken, , Op. cit., p. 129.Google Scholar