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VI.—On Singular Pencils of Zehfuss, Compound, and Schläflian Matrices

Published online by Cambridge University Press:  15 September 2014

W. Ledermann
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Extract

In this paper the canonical form of matrix pencils will be discussed which are based on a pair of direct product matrices (Zehfuss matrices), compound matrices, or Schläflian matrices derived from given pencils whose canonical forms are known.

When all pencils concerned are non-singular (i.e. when their determinants do not vanish identically), the problem is equivalent to finding the elementary divisors of the pencil. This has been solved by Aitken (1935), Littlewood (1935), and Roth (1934). In the singular case, however, the so-called minimal indices or Kronecker Invariants have to be determined in addition to the elementary divisors (Turnbull and Aitken, 1932, chap. ix). The solution of this problem is the subject of the following investigation.

Type
Proceedings
Information
Proceedings of the Royal Society of Edinburgh , Volume 56 , 1937 , pp. 50 - 89
Copyright
Copyright © Royal Society of Edinburgh 1937

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References

References to Literature

Aitken, A. C., 1935. “The Normal Form of Compound and Induced Matrices,” Proc. London Math. Soc., vol. xxxviii, ser. 2, pp. 354–376.CrossRefGoogle Scholar
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