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Given A an n x n matrix where the columns are the set of standard vectors S = {e1, e2,.....e_n} in R^n

These vectors are orthonormal according to the definition since

<e_i, e_j> = 0, i \neq j

<e_i,e_i> = 1

Since the columns of A then they are orthonormal according to the definition, and therefore the matrix A is orthogonal matrix which implies that

A^T A = I <---> A^ (-1) = A^T, and so on.

I need to show that the row vectors of of A are orthonormal too.

Any idears on how?

My own idear is that

Since

A^ (-1) = A^T, then the columns in invertible A become the rows in transposed A, and the these orthonormal according to the definition?

Sincerely Yours

Mathboy20

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# Homework Help: Orthonormal row vectors

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