# Tagged Questions

73 views

### Bounding the norm of the Dirichlet kernel as a matrix function

I asked the following there also, but I am beginning to think it would be more appropriate here. Consider the Dirichlet kerel: $f(x) = 1+2\sum_{k=1}^{N}\cos(kx)$. Now, given a diagonalizable real ...
202 views

### Determinant of $V^* V$ where $V$ is rectangular Vandermonde matrix with nodes on unit circle

Let $z_{1},\dots,z_{k}$ be distinct complex numbers with $\left|z_{j}\right|=1,\;j=1,\dots,k$. For any natural $N\geqslant k$ consider the rectangular Vandermonde matrix  V_{N}=\begin{pmatrix}1 ...
68 views

### The influence of eigendecomposition on the periodicity of a (rank 2) Hermitian matrix (of functions)

Let $\boldsymbol{R}(u,v);~u,v\in\mathbb{R}$ be a Hermitian matrix (of Hermitian functions) with entries r_{ij}(u,v) = 1 + Ae^{-2\pi i \phi_{ij}(ul_0 + vm_0)}; ...
644 views

### Eigenvalues of a sum of Hermitian positive definite circulant matrix and a positive diagonal matrix

Suppose I have a real $n\times n$ matrix $\mathbf{C}$ that is Hermitian, positive-definite, and circulant. We know that its eigenvalues $\{\lambda_0,\ldots,\lambda_{n-1}\}$ are extraordinarily nice ...
2k views

### How does the Laplace Transform work for circuit analysis? [closed]

I would like to understand how signals transformed from the time domain to the frequency domain for algebraic manipulation, can be transformed back to give solutions in the time domain. Knowing how to ...