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Results tagged with matrix-analysis
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user 9022
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.
1
vote
positive semidefiniteness: a psd matrix substracted by another rank 1 psd matrix
This is easy to formulate as a semidefinite programming problem.
First, let $X=xx^{T}$. The semidefiniteness constraint becomes
$A-\lambda X \succeq 0$
Next, use a standard technique to handle t …
- 3,934
7
votes
Accepted
Explicit formula for Cholesky factorization in a special case
The matrix $\alpha J$ is a rank one matrix, so there are simple update/downdate formulas for computing the Choleksy factorization of $Q+sI-\alpha J$ if you start with the factorization of $Q+sI$.
I …
- 3,934
1
vote
Norm bound on eigen-vector change caused by rank-one update
A tiny change can result in a shift of the dominant eigenvalue's eigenspace to something that is completely orthogonal to the dominant eigenvalue's eigenspace of $A$.
For example, let
$A=I-\epsil …
- 3,934