Is this a true statement or under some condition this is a true statement? I have try a dozen of MATLAB randomly generated real value square matrix, than take the QR decomposition to them, and all of orthogonal matrix obtained from QR decomposition seems satisfied this property, but I don't understand why this happened. Could anyone help me on this?
2026-03-30 02:07:06.1774836426
Prove or disprove the 2 norm for any column of an orthogonal matrix is smaller or equal to 1
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Hint. When $Q$ is an orthogonal matrix, how is the $j$-th diagonal element of $Q^TQ$ related to the entries of the $j$-th column of $Q$?