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Characterization of invariant subspaces using the notion of the Grassmann representative. (English) Zbl 1157.15007

This article contains only well-known, elementary linear algebra results with elementary proofs but in a slightly unconventional language and notation. The main result (rephrased to modern language) is that a \(k\) dimensional subspace of a finite dimensional vector space is invariant under a linear operator if and only if the \(k\)th exterior product of the subspace is invariant under the \(k\)th exterior product of the linear operator, where the only if part is only stated in a special case. This is also stated when the linear operator is of the form \(A+BF\) with no extra information for this special case.

MSC:

15A18 Eigenvalues, singular values, and eigenvectors
15A75 Exterior algebra, Grassmann algebras
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