Algebraic and Analytic Geometry
《Algebraic and Analytic Geometry》 · 第 209-210 页 · Section 4.2「Determinants of Order $n$」，Definitions
Definitions. Let $A\in M_{n\times n}(F)$. If $n=1$, so that $A=(A_{11})$, we define $\det(A)=A_{11}$. For $n\ge2$, we define $\det(A)$ recursively as $\det(A)=\sum_{j=1}^{n}(-1)^{1+j}A_{1j}\det(\tilde A_{1j})$. … The scalar $\det(A)$ is called the determinant of $A$ and is also denoted by $|A|$.