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Results tagged with matrices
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user 11361
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.
3
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1
answer
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Algorithmic Version of John's Decomposition of Convex Body
While reading textbooks on convex geometry, I heard about Fritz John's theorem on convex body, which is known as John's Theorem or John's Decomposition.
(I know that there are many variants, but this …
12
votes
3
answers
15k
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Kind of submultiplicativity of the Frobenius norm: $\|AB\|_F \leq \|A\|_2\|B\|_F$?
Let $\|\cdot\|_F$ and $\|\cdot\|_2$ be the Frobenius norm and the spectral norm, respectively.
I'm reading Ji-Guang Sun's paper 'Perturbation Bounds for the Cholesky and QR Factorizations' from BIT 3 …
19
votes
4
answers
7k
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Sherman-Morrison type formula for Moore-Penrose pseudoinverse
Given an $n\times n$ invertible matrix $\mathbf A$ and two column vectors $\mathbf u$, $\mathbf v\in\mathbb R^n$, suppose that $1 + {\mathbf v}^T {\mathbf A}^{-1}\mathbf u \neq 0$.
Then the Sherman-Mo …