Question: Let A be an m x n matrix whose columns are nonzero, mutually orthogonal vectors in Rm. (a) Explain why m > n. (b) Prove

Let A be an m x n matrix whose columns are nonzero, mutually orthogonal vectors in Rm.
(a) Explain why m > n.
(b) Prove that AT A is a diagonal matrix. What are the diagonal entries?
(c) Is A AT diagonal?

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