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Results tagged with linear-algebra
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user 4613
Questions about the properties of vector spaces and linear transformations, including linear systems in general.
21
votes
Nuances Regarding Naturality
The issue here is that the inverses to $V\rightarrow V^{**}$ and $V^*\otimes V\rightarrow \mathrm{Hom}(V,V)$ don't exist in the infinite dimensional case. So in order to show that they exist one has t …
- 3,137
8
votes
Accepted
Projecting a symmetric matrix onto the space of linear operators with a particular eigenvalue
Any (real) symmetric matrix may be diagonalised by an orthogonal matrix. So let your matrix be $A$ and let $O$ be an orthogonal matrix such that $D=OAO^{-1}$ is diagonal. Note that the transformation …
- 3,137