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Results tagged with linear-algebra
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user 5534
Questions about the properties of vector spaces and linear transformations, including linear systems in general.
2
votes
1
answer
847
views
What is the relationship between singular value decomposition and solving linear systems?
It is known that solving systems of linear equations is reducible to SVD in a straightforward way; if you want to solve $\mathbf{Ax}=\mathbf{b}$, then you can perform SVD on $\mathbf{A}$ and minimize …
- 2,019
13
votes
1
answer
1k
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A generalization of the Powers-Stormer inequality
The well-known Powers-Stormer inequality says the following: for positive semidefinite operators $A, B$, we have that $\mathrm{Tr}((A - B)(A - B)) \leq \| A^2 - B^2 \|_1$, where $\| \cdot \|_1$ indica …
- 2,019