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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.

6 votes
3 answers
1k views

Norm of the upper triangular part of symmetric matrix

Let $D\in \mathbb{R}^{n\times n}$ denote a lower triangular matrix. With $\|\cdot\|$ denoting the spectral matrix norm, is there an estimate like $$ \|D\| \leq C\|D+D^T\|, $$ where $C>0$ is independ …
11 votes
1 answer
524 views

LU factorization for $I+A$ (A skew-symmetric)

The matrix $M=I+A\in \mathbb{R}^{n\times n}$, where $I$ is the identity and $A=-A^T$ is skew-symmetric satisfies $$ Mx\cdot x = \|x\|^2 \quad\text{for all }x\in\mathbb{R}^n. $$ Therefore, $M=LU$ has …