How to show that if two basis B, B' are orthonormal basis of V, then the change of coordinate matrix $P^B_{B'}$ is an orthogonal matrix. I can understand it in the way that we rewrite $P^B_{B'}=\left(P^{B'}_\varepsilon\right)^{-1}P^B_\varepsilon$, but how to just directly understand it by $P^B_{B'}$ itself has orthonormal columns?
2026-03-30 02:05:46.1774836346
How to understand $P^B_{B'}$ an orthogonal matrix
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