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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.
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 …
- 867
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
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 …
- 165
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