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Inverse of Change of Basis Matrix

  1. Aug 17, 2011 #1
    Hi everyone,

    This is not a homework question.

    Let [itex]B_1[/itex] and [itex]B_2[/itex] be orthonormal bases. Let [itex]M[/itex] be the change of basis matrix from [itex]B_1[/itex] to [itex]B_2[/itex]. Then, is the inverse of [itex]M^{-1}[/itex] also a change of basis matrix? Namely, from [itex]B_2[/itex] to [itex]B_1[/itex]?

    At an intuitive level, I just assumed that was the case. Until I did some toy examples and it didn't seem to work out.

    What do you guys think?

    EDIT: Nevermind, I found a mistake in my calculation.
    Last edited: Aug 17, 2011
  2. jcsd
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