Question: Suppose S is an n x n matrix whose columns form an orthogonal, but not orthonormal, basis of Rn. (a) Find a formula for S-1

Suppose S is an n x n matrix whose columns form an orthogonal, but not orthonormal, basis of Rn.
(a) Find a formula for S-1 mimicking the formula Q-1 = QT for an orthogonal matrix.
(b) Use your formula to determine the inverse of the wavelet matrix W whose columns form the orthogonal wavelet basis (5.9) of R4.

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