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Results tagged with matrix-theory
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user 17261
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.
1
vote
Accepted
Choi type matrix condition for completely positivity on a certain operator system spanned by...
The answer is no :
Let $U_1 = I$, where $I$ is the identity and $U_2$ linear independent to $I$ such that $U_2^* + U_2 \ge 0$ .
Then choose $\phi(U_1) = I$ and $\phi(U_2) = -I$ .
- 2,753
18
votes
Is the linear span of special orthogonal matrices equal to the whole space of $N\times N$ ma...
Let $S$ be the span of $SO(N)$ .
Then it's obvious that if $A \in S$ and $D_1, D_2 \in SO(N)$ then $D_1^{-1} A D_2 \in S$ .
Therefore it's enough to show that $B := diag(1,0,...0) \in S$ .
If $N$ i …
- 2,753
7
votes
Accepted
Well known matrix inequality?
The desired inequality follows from an majorisation argument :
According to Bhatia Matrix Analysis Corollary III.4.6 we have :
$log \lambda(AB) \succ log \lambda^\downarrow(A) + log \lambda^\uparro …
- 2,753