Consider a $n \times n$ matrix $G$. Transform the column vector into an orthonormal basis by using the Gramm-Schmidt procedure, this produces a new matrix $Q$. Under which conditions is the column span (i.e, the image) generated by the first $m <n$ columns of $G$ same as the column span generated by the first $m$ columns of $Q$?
2026-04-01 00:41:24.1775004084
column span of a orthogonalized matrix is the same as the one of the original matrix?
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