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Results tagged with matrices
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user 38129
Questions where the notion matrix has an important or crucial role (for the latter, note the tag matrix-theory for potential use). Matrices appear in various parts of mathematics, and this tag is typically combined with other tags to make the general subject clear, such as an appropriate top-level tag ra.rings-and-algebras, co.combinatorics, etc. and other tags that might be applicable. There are also several more specialized tags concerning matrices.
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Accepted
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
votes
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