### Diagonalizability of the product versus diagonalizability of the individual factors

#### Abstract

The following question is attempted: Given two commuting matrices $A$ and $B$ with complex (real) entries such that $AB$ is unitarily (orthogonally) diagonalizable, when will it happen that $A$ and $B$ are diagonalizable?

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PDF#### References

R. Horn and C. Johnson, emph{Matrix Analysis}, $2^{nd}$ edition, Cambridge University Press, 2012.

C-K. Li and S. Pierce, emph{Linear preserver problems}, The American Mathematical Monthly, (August-September) (2001), 591-605.

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