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Results tagged with determinants
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user 38129
Questions about the determinant of square matrices or linear endomorphisms. Also for closely related topics such as minors or regularized determinants.
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Determinant inequality of square-product sum of diagonal matrix and upper-triangular matrix
I have found the proof by mathematical induction. Thanks to Sean Shih and Chu-Lan Kao for fruitful discussions.
For $n=1$, the inequality is obvious.
Suppose that for $n=m\in\mathcal{N}$, $\det(\mat …
- 51
4
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1
answer
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Determinant inequality of square-product sum of diagonal matrix and upper-triangular matrix
Recently, I have seen a matrix inequality but don't know how to prove it. The inequality goes as follows.
For an arbitrary $n\times n$ diagonal matrix $\mathbf{D}$ and an arbitrary upper-triangular m …
- 51