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#1

$Old$ November 3rd, 2009, 10:38 PM

amm345 $amm345 is offline$

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$Default$ General Linear Group Proof Help

Let

A ∈ Mn(F).
Prove that A ∈ GLn(F) if and only if the columns of A form a basis for Fn.

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#2

$Old$ November 4th, 2009, 02:55 AM

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$GL_n(F)$ is the group of invertible n by n matrices on F. The columns of a matrix span the image of the matrix in $F^n$ . If those columns form a basis for $F^n$ , then the image is the entire space and so the matrix is invertible.

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