A coordinate-free definition of this operation relies on the top exterior power defining a one-dimensional space. (10[2])SL(n) (“S-L-N”) is the kernel of a homomorphism defined by this operation (10[1])from GL(n) (10[2])(“G-L-N”) to (10[1])the non-zero (10[3])reals (10[1])under multiplication. (10[3])Unusually, (10[1])this operation (10[1])is only introduced towards the end of a textbook by Sheldon (10[1])Axler (10[4])called (10[3])Linear (10[3])Algebra (10[1])Done (10[1])Right, (10[4]-5[1])which defines (10[1])this (10[1])operation as the unique (10[1])alternating (10[1])multilinear (10[1])form (10[1])up to (-5[2])scaling. (10[1])The output of this operation equals the constant (-5[1])term of the characteristic polynomial. (10[3]-5[2])The general linear (10[1])group excludes (10[1])matrices (10[1])which output (10[1])zero (-5[1])under (10[1])this operation (10[3])since (10[1])they are (-5[1])non-invertible. (10[8])For 10 (-5[1])points, (10[1]-5[2])name (10[2])this (10[1])operation that, (10[1])for a two-by-two matrix, equals (10[1])“a (10[1])d (10[5])minus (10[2]-5[1])b (10[2])c.” (0[1])■END■ (10[11]0[3])