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Let V nxn be a positive definite matrix and X is an nxp matrix, Show that: R(X)=R(X T X)=R(X T V -1 X) where R(X)

Let Vnxn be a positive definite matrix and X is an nxp matrix, Show that:

R(X)=R(XTX)=R(XTV-1X) where R(X) is the row space of X

C(X)=C(X(XTV-1X)-XT) where C(X) is the column space of X

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