Imagine we have given a matrix $A$ and an index (row,column);
Is is then possible to find an orthogonal matrix $Q$ such that $AQ$ has only zeros in line 'row' except the 'columnth entry'?
2026-03-29 11:06:58.1774782418
Is it possible to find for every matrix $A$ an orthogonal matrix $Q$ such that $A*Q$ has only one entry in some row?
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Yes. Say we're working on the field $\Bbb{R}$. The line you chose can be identified as a vector $v\in{\Bbb{R^n}}$. The orthogonal space of ${v}$ is a vector space of dimension $n-1$, just take any base of it. Define $Q$ to be the matrix whose coloumn you chose is $v$, and put the base you picked on the rest of its coloums.