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Reduction of Singular Pencils of Matrices1

Published online by Cambridge University Press:  20 January 2009

W. Ledermann
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Let ρA + σB =[ραμν + σbμν] be a pencil of type m × m′, i.e. with m rows and m′ columns, where A and B are matrices with constant elements which are not mere scalar multiples of each other; and ρ and σ are homogeneous parameters.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 4 , Issue 2 , January 1935 , pp. 92 - 105
Copyright
Copyright © Edinburgh Mathematical Society 1935

References

page 92 note 2 CfTurnbull, and Aitken, Canonical Matrices (1928), p. 125ff, where references may be found.Google Scholar

page 93 note 1 CfTurnbull, and Aitken, Canonical Matrices, Chapter IX.Google Scholar

page 93 note 2 Bromwich, however, deals with the general case (Proc. London Math. Soc. (1), 32 (1900)).Google Scholar

page 100 note 1 By saying the stair is of length l, we mean that it consists of l vectors and cannot be continued by another vector.