The determinant of a linear transformation $T: V\to V$ (where $V$ is finite-dimensional) is the unique antisymmetric $n$-variable multilinear map $\text{det}$ such that \(\text{det}:(\mathbb R^n)^n \to \mathbb R\) such that $\text{det}(e_1,\dots,e_n)=1$. It is defined for a the matrix $A$ of $T$ as \(\text{det}(A) = \text{det}(A_1,\dots,A_n)\) where the $A_i$ are the columns of $A$.
Wikidata ID: Q178546