If
is an orthonormal set in an inner product space V, and
is a
orthogonal matrix, then
is also an orthonormal set in V.

Name: If is an orthonormal set in an inner product space V, and is a orthogonal matrix, then is also an orthonormal set in V.
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Question

If 
  is an orthonormal set in an inner product space V, and 
  is a 
  orthogonal matrix, then 
  is also an orthonormal set in V.

Quizplus · Accepted Answer

An orthogonal matrix preserves orthonormality of vectors, so if one orthonormal set is transformed by an orthogonal matrix, the resulting set will also be orthonormal.

If Is an Orthonormal Set in an Inner Product