# Tagged Questions

The tag has no wiki summary.

31 views

### Lanczos algorithm with thick restart on a dynamic matrix

currently, I'm working on a way to compute the 2 biggest eigenvalues of a real, symmetric, huge and sparse matrix that changes a few entries from time to time. The problem should be solved using an ...
66 views

### Eigenvalue of (0-1) matrix

Assume I have 2 matrices, each of size nxn with only 1 and 0 as entries in both. (n>10) The first matrix (call it A) has each row summing up to 2 (ie: on each row, it has two "1" and n-2 "0"). It is ...
107 views

203 views

### Eigenvalues of an amplification matrix

Let $A$ and $B$ square real matrices. I know that the matrix $A+B$ has 1 as eigenvalue of multiplicity 1 and the others eigenvalues have their modulus <1. Can we say something about the eigenvalues ...
140 views

### Can an accumulation point be an eigenvalue?

For an discrete (separable) infinite-dimensional Hilbert Space with a compact operator, 0 is always an accumulation point (https://www.math.ucdavis.edu/~hunter/book/ch9.pdf). Does this mean its part ...
107 views

### nodal lines in the dirichlet problem

In the Dirichlet problem if nodal lines do not touch $\partial\Omega$ (unit disk), what happens to the eigenvalues? Thanks for help.
61 views

### On generalization of Wigner semi circle

I want to analyse noise model for a matrix M whose entries are not real numbers. The matrix is a collection of N permutation matrices of size nxn i.e, M is NnxNn. Because its a collection of ...
160 views

### eigenvalues of two nonnegative matrices

Let $A$ and $B$ be symmetric non-negative matrices. If $A\geq B$ (i.e., $A-B$ is a nonnegative matrix), can we say that $\lambda_i(A) \geq \lambda_i(B)$ for all $i$, where $\lambda_i$ denotes the ...
475 views

### Non symmetric matrices with real eigenvalues

Consider the following block matrix $A=\pmatrix{A_1 & A_2\cr kA_2^\top & A_3}$ where $A_1$ is a symmetric matrix, $A_3$ is diagonal matrix and all entries of $A$ are real and non-negative. ...
68 views

### Characterizing the singular values of a matrix with structure

Suppose we have a function from $\mathbb{R}^2\to\mathbb{C}$, $$f(x,y) = e^{\imath\pi x g(y)}$$ where $g(y)$ is periodic in $y\in[-T, T),\ T<\infty$ (e.g., a sinusoid) and $0\leq x < \infty$ ...
184 views

### Multiple eigenvalues over imperfect fields

Let $K$ be a field. For a matrix $A\in GL_n(K)$ we can find the Jordan normal form $A'$ in $GL_n(\overline{K})$, where $\overline{K}$ is the algebraic closure of $K$. We write $j_\alpha(A)$ for the ...
148 views

### Summation of eigenvalues of tri-diagonal matrix smaller than specific value

Is there any analytic expression for summation of eigen-values of a tri-diagonal matrix which are smaller than a constant value? Or even a rough approximation for it. How about case of a general ...
63 views

### Eigenvectors of contraction times projection

Suppose $A$ is a real $n\times n$ matrix with real eigenvalues: $$1=\lambda_1>|\lambda_2|\ge \ldots\ge |\lambda_n|>0.$$ Suppose $B$ is an involution, for simplicity let us assume that $B$ is ...
103 views

### Spectrum of a Laplacianized matrix

Suppose that $A$ is a positive matrix and that we let $R$ be the diagonal matrix of $A$'s row-sums. What can be said about the spectrum of $R-A$? I am particularly interested in the largest eigenvalue ...
65 views

### Laplacian using SDP

Is there any suggestion about how could one construct a model that uses semidefinite programming that minimizes sum of k smallest eigenvalues of Laplacian matrix? I found two papers that have done ...
466 views

### Relating the angle between two vectors to max and min eigenvalues

Hi. I am busy working through a paper i came accross online on portfolio optimization. The paper may be accessed on the following link: http://ssrn.com/abstract=1483412 I am struggling, in ...
84 views

### Ratio of Eigen values and Mutual Independence

Given a matrix $X$. Calculating the Eigen values of $XX^T$ and using the ratio of maximum and minimum eigen values normally gives the condition number of the matrix. If $X$ contains $M$ observations ...
130 views

### The smallest eigenvalue from an equitable partitions

Suppose that $G$ is a connected graph with equitable partition $\pi$. Then the eigenvalues of the divisor multigraph $G / \pi$ are all eigenvalues of $G$. (Perhaps excluding some pathological cases) ...
263 views

### Condition for block symmetric real matrix eigenvalues to be real

I have a (2nx2n) block symmetric matrix that in the simplest case (n=2) looks like:  M_2 = \begin{bmatrix} a_1 & 0 & b_{1,2} & -b_{1,2}\\\ 0 & -a_1 & b_{1,2} & -b_{1,2}\\\ ...
640 views

### Upper bounds on eigenvalues of PSD matrix?

Suppose A is a symmetric positive semidefinite matrix. Is there a way to upper bound the largest eigenvalue using properties of its row sums or column sums? For instance, the Perronâ€“Frobenius ...
611 views

### Singular Value Decomposition of Noisy Matrices

I am an engineer who makes measurements of a variable over a grid of, say, $m\times n$. Since these are actual measurements, the true values are always corrupted by noise, and what I measure is a ...
625 views

### Eigenvalues of a Symmetric Positive Semi-Definite (PSD) matrix after rank one update

I have a Symmetric Positive Semi-Definite matrix $A$ which i know its eigenvalue and eigenvectors. let $v$ and $u$ be a random column vector. i want to know if it is possible to have eigenvalues of ...
239 views

### Checking whether this would be bounded

It may be better to post this question here. Assume that $M$ is an $m$ by $m$ ($m$ is an even number) symmetric positive-semi-definite matrix with exactly $m/2$ positive eigenvalues and every entry of ...
434 views

### can eigenvector be found without computing the eigenvalue [closed]

Is there any ways to compute the eigen vector without computing explicitly the associated eigenvalue? Actually, I'd like to compute the largest eigenvalue of a positive matrix from its eigen vector, ...
339 views

### Prove log of eigenvalues are dense in R?

Suppose you have the set of all possible $n$ x $n$ square adjacency matrices where $n$={1,2,3,4...}. For each matrix, compute the logarithm of the largest eigenvalue. Is it true that the set of ...