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- Thread starter IniquiTrance
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[tex]det(X^TX) = det(X)^2=0[/tex]

If not X is not square, but is real, then QR decomposition should reduce the problem to that of square matrices (something simpler may suffice, but this is the simplest approach I can think of right now).

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AlephZero

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Thank you. I suspected it was true, but couldn't prove it to myself.

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That's a very nice proof, especially because you established necessary and sufficient conditions. The OP claimed that he could prove the converse, but, if he knew this proof he should have had no trouble.

Just one remark, instead of "contradiction", maybe you should have used "contraposition".

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AlephZero

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Well, I used to know what "contrapositive" meant when I was a student, but these days I find understanding the concepts is more useful than remembering their names.Just one remark, instead of "contradiction", maybe you should have used "contraposition".

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