Question
Let $U$ be an orthogonal matrix, and construct $V$ by inter-changing some of the columns of $U .$ Explain why $V$ is an orthogonal matrix.
Step 1
This means that all columns of $U$ are orthogonal to each other and each column has a norm of 1. In mathematical terms, if $u_i$ and $u_j$ are columns of $U$, then $u_i \cdot u_j = 0$ for $i \neq j$ and $||u_i|| = 1$ for all $i$. Show more…
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