invert or transpose

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Is this correct:

When finding the diagonalization of a matrix $A$ of the form $QDQ^{-1}$ then if you normalize your eigenvectors instead of having to invert $Q$, you could just take $Q^t$.

Just because I did not know what so search for online.

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It's not always correct! The inverse $Q^{-1}$ is equal to $Q^T$ only for an orthogonal matrix. A matrix $A$ is diagonalizable via an orthogonal matrix $Q$ i.e. $$A=QDQ^T$$ only if $A$ is symmetric.