Question

A little question about orthonormal basis.

Answer 1

I was reading a book and I find:
If B and B' are orthonormal basis then:
\[\left [ B' \right ]_{B}^{-1}=\left [ B' \right ]_{B}^{t}\]
I was using:
C={(1,0,0),(0,1,0),(0,0,1)}
B={(1/3^(1/2),1/2^(1/2),1/2^(1/2)),(-1/3^(1/2),0,-1/2^(1/2)),(1/3^(1/2),1/2^(1/2),0)} And \[\left [ B' \right ]_{C}^{-1}\neq\left [ B' \right ]_{C}^{t}\]
What's wrong?