Is the definition of an orthogonal matrix:(adsbygoogle = window.adsbygoogle || []).push({});

1. a matrix where all rows are orthonormal AND all columns are orthonormal

OR

2. a matrix where all rows are orthonormal OR all columns are orthonormal?

On my textbook it said it is AND (case 1), but if that is true, there's a problem:

Say we have a square matrix A, and we find its eigenvectors, they are all distinct so A is diagonalizable. We put the normalized eigenvectors of A as the columns of a matrix P, and (our prof told us) P becomes orthogonal and P^-1 = P^T. My question is how did P become orthogonal straight away? By only normalizing its columns how did we guarantee that its rows are also orthonormal?

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# Orthogonal Matrix

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