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Let \(A\) be a square matrix of real numbers whose columns are (non-zero) orthogonal vectors.
a) Show that \(A^{T} A\) is a diagonal matrix - whose inverse is thus obvious to compute.
b) Use this observation (or any other method) to discover a simple general formula for the inverse, \(A^{-1}\) involving only its transpose, \(A^{T}\), and \(\left(A^{T} A\right)^{-1}\). In the special case where the columns of \(A\) are orthonormal, your formula should reduce to \(A^{-1}=A^{T}\).
in Mathematics by Platinum (129,882 points) | 216 views

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asked Jan 21 in Mathematics by MathsGee Platinum (129,882 points) | 219 views
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