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Results tagged with linear-algebra
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user 20341
Questions about the properties of vector spaces and linear transformations, including linear systems in general.
2
votes
0
answers
104
views
Angle between subspaces in indefinite signature
I know there is a notion of principal angles between subpaces of a Euclidean space, but what about subspaces of a finite dimensional vector space $V$ equipped with a non-degenerate quadratic form of i …
- 452
12
votes
Geometric interpretation of trace
It has been said before but let me rephrase it : the interpretation of the trace is not geometric but integration-theoretic (I do not say "measure-theoretic since there is no measure, see below). Of c …
3
votes
Given a subdomain of GL(n), when is the map from matrices to their matrices of eigenvectors ...
Whatever the way you define your map, you cannot expect a diffeomorphism for dimension reasons. The simple fact that you can rescale your eigenvectors makes you lose some dimensions (at least n). In a …
- 452
6
votes
4
answers
879
views
A name for matrices with only simple eigenvalues?
I am constantly working with hermitian matrices without multiplicity in their spectrum. Since this hypothesis appear in several important problems, for instance perturbation theory, I looked in the li …
- 452