Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-15T23:38:05.676Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

1. Baer, R., A unified theory of projective spaces and finite abelian groups, Trans. Amer. Math. Soc. 52 (1942), 283–343.Google Scholar
2. Baer, R., Linear algebra and projective geometry (New York, 1952).Google Scholar
3. Birkhoff, G., Lattice theory, Amer. Math. Soc. Colloquium Publications, Vol. XXV (1948).Google Scholar
4. Hoffman, K. and Kunze, R., Linear algebra (Englewood Cliffs, N.J., 1961).Google Scholar
5. Jacobson, N., Lectures in abstract algebra, Vol. II (Princeton, N.J., 1953).Google Scholar