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Results tagged with matrix-analysis
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user 68572
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.
5
votes
Accepted
Upper bounds on elements of a matrix
$C$ is an idempotent matrix, so its eigenvalues are either 1 or zero. $C$ is also Hermitian so Schur's Theorem says the sum of the $k$ largest eigenvalues is greater then the sum of the $k$ largest di …
- 131
4
votes
Accepted
Eigenvector of a nonnegative matrix in closed form
If you write $A\nu=\nu$ as a system of equations it can be written as
$$
\frac{\nu_i}{1-\alpha_i}=\sum_{j=1}^{n}\frac{\alpha_i\nu_j}{1-\nu_j}
\qquad \forall i=1, ..., n.
$$
Then the change of variabl …
- 131