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I am arguing with a friend about the following:

He claims that if a mxn matrix A, m>=n has a reduced QR-decomposition where R has j nonzero diagonal elements, then the rank of A is at least j. I claim that it is exactly j.

It was some years ago since i read linear algebra so i was hoping someone here could help us out.

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# If a mxn matrix A, m>=n has a reduced QR-decomposition

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