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Results tagged with matrix-analysis
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user 102946
The study of the properties of real and complex matrices that are more close to analysis and operator theory. For instance: the properties of positive definite matrices, matrix inequalities, perturbation analysis, matrix functions, inequalities between eigenvectors and singular values, majorization.
58
votes
Accepted
Is this proof of Perron's theorem correct, and if so is it original?
(1) Correctness: I read all arguments in detail and couldn't find anything wrong with them. Of course, this doesn't mean too much...
(2) Orginality: I think in a topic which has such an extensive his …
- 12.6k
7
votes
Accepted
On approximate simultaneous diagonalization
The answer is no in general.
For a $2\times 2$-counterexample, let $A = 0$, let $B$ be the diagonal matrix with diagonal entries $1$ and $0$ (i.e. $B$ is the projection onto the first component), cho …
- 12.6k
4
votes
Accepted
A matrix monotonicity question
The answer is no, in general. Here is a counterexample:
Let
\begin{align*}
X =
\begin{pmatrix}
1 & 0 \\
0 & 0
\end{pmatrix},
\quad \text{and} \quad
A =
\begin{ …
- 12.6k