MathGloss

The determinant of a linear transformation T:VVT: V\to V (where VV is finite-dimensional) is the unique antisymmetric nn-variable multilinear map det\text{det} such that det:(Rn)nR\text{det}:(\mathbb R^n)^n \to \mathbb R such that det(e1,,en)=1\text{det}(e_1,\dots,e_n)=1. It is defined for a the matrix AA of TT as det(A)=det(A1,,An)\text{det}(A) = \text{det}(A_1,\dots,A_n) where the AiA_i are the columns of AA.

Wikidata ID: Q178546