# Tagged Questions

30 views

### Eigenvalues that are functions

Let us have the Laplacian on a compact manifold $M$. Suppose I have some equation of the form $$-\Delta u(x) = f(x)u(x).$$ If $f \equiv c$ were a constant, this would be an eigenvalue problem ...
45 views

### What is known about the eigenvectors of random matrices?

Let $A$ be a real asymmetric $n \times n$ matrix with i.i.d. random, zero-mean elements. What results, if any, are there for the eigenvectors of $A$? In particular: How are the elements of the ...
47 views

351 views

### Min Max Principle and Rayleigh-Ritz-Method for eigenvalues of unbounded operators?

Finding eigenvalues of matrices using the Rayleigh-Ritz quotient is well-known, c.f. http://en.wikipedia.org/wiki/Min-max_theorem Does the following generalization of that fact also hold? Theorem: ...
167 views

### Reference suggestion: eigenvalues of tridiagonal matrices

I would like to ask for a reference on the problem of computing the eigenvalues/eigenvectors of tridiagonal matrices (not necessarily with constant diagonals). I have seen authors use continued ...
189 views

### Is there a great book on eigenvalues?

I keep encountering ostensibly very different branches of mathematics, only to have eigenvalues show up in each one. Is there a single book out there that presents a deep, unified account of the ...
23k views