# Tagged Questions

For questions about matrices which are defined block wise, like $\pmatrix{A&B\\ C&D}$ where $A,B,C$ and $D$ are themselves matrices. Use this tag with (matrices), and often with (linear-algebra).

59 views

### Find signature of symmetric block matrix, given the diagonal blocks are positive / negative definite - Check my proof

This may be a basic question, but I'd like someone to double check it. We are given the matrix $A=\begin{pmatrix} A_1 & C \\ C^T & A_2\end{pmatrix}$ where $A_1$ is a $k$ by $k$ positive ...
83 views

41 views

### Condition for a block matrix to be positive semi-definite

Let's say we have two positive semi-definite matrices $A$ and $B$ and a negative real $\lambda$. What would be the conditions for the matrix $M$, defined as follows, to be positive semi-definite too ? ...
29 views

7 views

### Solving Toeplitz plus Diagonal System, how should I make use of the structure?

I learned that a Toeplitz system, $Ax = B$ where $A$ is Teoplitz, can be solved in $O(n \log n)$ time using Superfast method. or approximate $A$ similar to Approximation method. I am keep ...
28 views

### Computing characteristic polynomial of tridiagonal block matrices

I want to compute the characteristic polynomial of symmetric matrices of the form \begin{bmatrix} A & U & & & 0\\ U & B & V & &\\ & V& C& W &\\ ...