# Tagged Questions

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.

380 views

### Null Space Perturbations

Hi, I face a problem some time now (not a homework problem) and I believe it is related to matrix perturbations and how the null space behaves in these cases. The distilled version of the ...
230 views

### Bandwidth reduction of multiple matrices

Suppose I have a symmetric matrix A, and several diagonal matrices $D_1,D_2,...$ Are there any matrix transformations, such as $P^\top A P$ so that $P^\top AP$, $P^\top D_1 P$, $P^\top D_2 P$, etc ...
384 views

### Perron Frobenius with one negative pair of entries

Suppose you have a real symmetric matrix $A$ which is positive except for $a_{ij},a_{ji}$, who are negative. While it is not generally true that the eigenvector of the dominant eigenvalue of $A$ is ...
675 views

### A matrix diagonalization problem

For matrices $X,Y\in [0,1]^{n\times m}$, for n > m, is there a square matrix $W\in R^{n\times n}$ so that $X^TWY$ is diagonal if and only if $Y = X$? Furthermore, $X$ and $Y$ are column normalized so ...
1k views

### How about eigenvalues of a positive matrix and a positive rank one matrix

Assume that A, B are positive n by n matrices and the rank of B is 1, B=xx*. If the eigenvalues of A are a_1≥a_2≥...≥a_n, and x is not the eigenvector of A, then there are d_i≥0 such that eigenvalue ...
7k views

### How to compare two similarity matrices?

Hi, Suppose that I have two nxn similarity matrices. These matrices contain similarity information between n items. Although both matrices contain similarities of the same n items they do not contain ...