I'm reviewing the spectral decomposition theorem. If $Y$ is a symmetric matrix, then $Y$ can be decomposed as $Y=Q\Lambda Q'$, where the columns of $Q$ are the eigenvectors of $Y$ and $\Lambda$ is a diagonal matrix with the diagonal composed of the eigenvalues of $Y$.
From some part of this theorem can it be concluded that $Q$ is an orthogonal matrix? I know that the eigenvectors of $Y$ are orthogonal, so can it be concluded that the matrix $Q$ is orthogonal?
from Hot Weekly Questions - Mathematics Stack Exchange
Javier Mariño
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