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The Invariant Subspace Lattice of a Linear Transformation

Published online by Cambridge University Press:  20 November 2018

L. Brickman  and
P. A. Fillmore
L. Brickman
Affiliation:
Indiana University, Bloomington, Indiana
P. A. Fillmore
Affiliation:
Indiana University, Bloomington, Indiana
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The purpose of this paper is to study the lattice of invariant subspaces of a linear transformation on a finite-dimensional vector space over an arbitrary field. Among the topics discussed are structure theorems for such lattices, implications between linear-algebraic properties and lattice-theoretic properties, nilpotent transformations, and the conditions for the isomorphism of two such lattices. These topics correspond roughly to §§2, 3, 4, and 5 respectively.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 19 , 1967 , pp. 810 - 822
Copyright
Copyright © Canadian Mathematical Society 1967

References

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