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Results tagged with matrix-theory
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user 36688
Matrix theory is the study of matrices as concrete objects, rather than as abstract linear operators between vector spaces (whose study belongs to linear algebra). For instance, this involves matrix factorizations and decompositions, nonnegative matrices and Perron-Frobenius theory, Schur complements, structured and special matrices, matrix functions and equations.
3
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0
answers
255
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Homotopicity of $a\mapsto a\otimes 1$ and $a \mapsto 1\otimes a$ as morphisms from $A$ to $A...
let $A$ be a $C^*$ algebra. We equip $A\otimes A$ with the spatial norm.
Assume that two morphisms $a\mapsto a\otimes 1$ and $a \mapsto 1\otimes a$ are homotopic morphisms, i.e, there is a curve $ …
- 356
2
votes
Is the linear span of special orthogonal matrices equal to the whole space of $N\times N$ ma...
It is sufficient to prove the statement in the question only for matrices in the form $[1]_{1\times 1}\oplus [0]_{k}$, that is the rank-1 projections or $$\begin{pmatrix} 0&\lambda\\ -\lambda …
- 356
6
votes
1
answer
751
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Is every real matrix conjugate to a semi antisymmetric matrix?
Is it true to say that every matrix $A\in M_n(\mathbb{R})$ is similar (conjugate) to a matrix $B=(b_{ij})$ with $b_{ij}=-b_{ji}$ for all $i\neq j$?(With some abuse of terminology,a matrix $B$ with th …
- 356