For any real matrix $A$, write down a sufficient condition for a real matrix $E$ to exist such that $E^2 = A$, and prove that this condition is sufficient.
How would I go about answering this question? I need a starting point please
2026-03-29 13:27:39.1774790859
Square root of of real matrices
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Hint: you might start by investigating the case of diagonal matrices. Then generalize a bit to diagonalizable ones.
On the other hand, examples such as $\pmatrix{-1 & 0\cr 0 & 1\cr}$ and $\pmatrix{0 & 1\cr 0 & 0\cr}$ that have no real square root show you can't generalize too far.