# Tag Info

### Finding value of unknown coefficient such that a linear system has a number of solutions

Here is a bit of an unconventional approach, but I think it works nicely here: Take the first two equations and transpose them: $2x+y=1-3z$ $(1)$ $x+2y=2-2z$ $(2)$ Now, solve these for $x$ and $y$ in ...
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### How to solve abstract matrix equations involving transposes and inverses?

These are pretty much the main things to keep in mind: Matrix addition works exactly the same as you'd expect. You can add or subtract matrices from both sides of an equation. Matrix multiplication ...
1 vote

### What is the square root of a square matrix squared?

You already can't conclude this for ordinary real or complex numbers; the best you could possibly ask for is that $A = \pm x$ (by which I mean $A = \pm x$ times the identity matrix). But actually you ...
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### A general solution $M$ for the matrix equation $A^* M^* + M A = 0$
This is indeed a Sylvester-like equation, but the adjoint on $M$ prevents us to solve it in the same general way $-$ apart from particular solutions such as $M = iA^\dagger$ or by assuming that $M$ is ...