= Determinantal function
{title2=$D(I_n)=1$}
A <determinantal function> on $M_n(F)$ is an <alternating multilinear map> of the $n$ columns, normalized to take value one at the <identity matrix>. It is uniquely the <determinant>. Indeed, expand each column in the <standard basis>. Terms with a repeated <basis vector> vanish, and all remaining terms differ from the value on the <standard basis> only by the sign of a <permutation>. Thus an <alternating multilinear map> of $n$ columns is determined by its value on the <identity matrix>.
Back to article page
