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proposition: $T^TB T$ is diagonal, if $T$ is not orthogonal, then we orthogonalize $T$, and $T$ becomes $T1$, then $T1^TB T1$ is still diagonal

Is it right, when it's right?

$T$ is transpose

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To integer: how do we orthogonalize $T$? – Robert Lewis Oct 6 '13 at 8:02
If $T^T B T$ is diagonal, then $T^T B T$ is diagonal. Could you state more carefully what you are asking? – Hurkyl Oct 6 '13 at 8:07

In general not: you have to orthogonalize the eigenvectors of each eigenspace separately.

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