Can anyone please show a proof for the following:
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Given the upper $m\times n$ block $U^{m\times n}$ of a real $n\times n$ unitary matrix $U^{n\times n}$, prove that:
(a) there always exist in $U^{m\times n}$ a subset of $m$ linearly independent (non zero) columns (not necessary consecutive),
(b) such subset is always unique / may not be unique ?
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Thanks in advance.