# Tagged Questions

Questions related to equations, with matrices as coefficients and unknowns.

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### Find non-diagonal matrices $A$ and $B$ such that $B^TAB$ is diagonal

Here $B^T$ denotes the transpose of $B$. $A$ and $B$ are invertible $3\times 3$ matrices with integer entries. $A$ is symmetric positive definite with at most two zero entries. We want the ...
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### Linearize Matrix Equation

I want to find a linearized formula for G in terms of A. $G = B^TC^{-1}T(I+BA)$ $G$ is 4x2 $B$ is a constant matrix 2x4 $A$ is a variable matrix 4x2 $C = I + A^TB^T + BA + BAA^TB^T$, so $C$ is ...
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### how to solve an matrix equation that is similar to a sylvester equation

during an algorithmn, I have to solve an equation of the form $$AXD-XBD=C$$ with $A\in\mathbb{R}^{n\times n}$,$X\in\mathbb{R}^{n\times m}$,$B\in\mathbb{R}^{m\times m}$,$D\in\mathbb{R}^{m\times p}$ and ...
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### projectors solution of a matrix equation

If I have two n*n dimensional complex matrix A and B, A and B are both projectors. i.e., A^2=A and B^2=B. If A*B=A and A is not identity, clearly if B=A, or B=I then the equality holds, can B has ...
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### If $X$ is zero matrix,what is $e^X$?
Let $X$ be an n×n real or complex matrix. The exponential of $X$, denoted by $e^X$, is the n×n matrix given by the power series $e^X =\sum_{k=0}^{\infty} X^k/k!$ where $X^{0}$ is defined to be the ...