## New answers tagged matrix-equations

28
votes

### Is there a "weak" fundamental theorem of algebra for matrices?

Although what you are asking for is not true, there is a very interesting related fact that is true. Let $k$ be an algebraically closed field of any characteristic. The theory of matrix factorisations ...

15
votes

Accepted

### Is there a "weak" fundamental theorem of algebra for matrices?

No, for rather trivial reasons. Consider the polynomial $f(X) = \varepsilon X - 1$ with $\varepsilon^2 = 0$, $\varepsilon \neq 0$, in $R = M_2(\mathbb{C})$. Then a root of $f(X)$ would mean that $\...

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