# 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).

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### 2nd order Matrix differential equation

$\ddot{X}+W\dot{X}=X$, $W$ is n-dimensional skew symmetric matrix. $X$ is a column vector and $I$ is identity matrix of appropriate dimension. \left(\begin{array} XX \\ \dot{X} ...
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### most general form of $X - A = X^{-1}B (X^{-1}BX^{-1}+ C)^{-1}$ that has a real solution $X = f(A,B,C)$?

What is the most general form of the cubic matrix equation $X - A = X^{-1}B (X^{-1}BX^{-1}+ C)^{-1}$ that has a real solution of the form $X = f(A,B,C)$, where $A,B$ and $C$ are positive definite ...
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### 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 &\\ ...
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### Sorting Matrix to Block structure

I have a symmetric matrix and I want it to be as block-like as possible. I don't have a clear definition. I want the smallest number of groups of non zero elements or maybe the most non-zero elements ...
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### Characteristic polynomial of triangular blocks matrix

Let A be a triangular blocks matrix (the blocks are: A1,...,Ak). Show that CA(t)=CA1(t)*...*CAk(t). Any help ? thanks ;) (edit: CA and CAj are the characteristic polynomials of the blocks)
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### Block Diagonalization related to Direct Sum and Single Eigenvalue?

I'm just a beginner in Linear Algebra, and I've proved myself the following: A matrix $A^{n \times n}$ is block diagonalizable if and only if the base field $F^n$ can be divided into at least two ...
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### Block Diagonalisation of 4x4 Matrix

I'm attempting to find a 4x4 matrix, P, that will convert my matrices, $A = \begin{bmatrix}1&1&0&0\\0&-1&0&0\\0&0&-1&0\\0&0&0&-1\end{bmatrix}$ and, ...
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### Matrix diagonalization theorems and counterexamples: reference-request.

I'm looking for exhaustive list of diagonalization theorems and counterexamples in linear algebra. In this question I understand the question of matrix diagonalization very broadly: suppose we have ...
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### Eigenvalues of a submatrix

A self-adjoint matrix $A$ in a complex linear space has real eigenvalues bounded between $0$ and $1$. If $A$ is projected onto an arbitrary two-dimensional subspace, what would be the bounds on the ...
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 ? ...