# Tagged Questions

52 views

### Finding the smallest max eigenvalues for related matrices?

While messing around with a spectral approach to a graph coloring question, I happened upon a type of problem I hadn't seen before. Suppose you have two symmetric $n$ x $n$ matrices in the form ...
17 views

### Motivations for Shi-Malik Algorithm

So I've been trying to make sense of the clustering algorithm on page 6 of this paper. Are the "first" k eigenvalues they refer to the smallest eigenvalues? What are the $y_i$ exactly? I don't see ...
36 views

From Norman Biggs, Algebraic Graph theory 2j, p13: The adjacency matrix has a spectral decomposition $A = \sum \lambda_aE_a$, where the matrices $E_a$ are idempotent and mutually orthogonal. (...) It ...
29 views

### Eigen vectors of graph laplacians

I have been reading about spectral graph theory from Daniel A. Spielman's notes. Fiedler’s Nodal Domain Theorem from this note says that : Let $G = (V, E, w)$ be a weighted connected graph, and let ...
41 views

### Lower bound on the minimum eigenvalue of sum of two matrices

Assume that $A$ is a symmetric positive definite matrix and $B$ is a symmetric (can potentially negative entries). Is the following bound correct? \lambda_{min}(A+B)\geq ...