Determinants
Table of Contents
1 Definition
We define the determinant of an \( n \times n \) square matrix as follows:
\[ det(A) = \sum_{\sigma \in S_n} sgn(\sigma) \prod_{i=1}^{n} A_{i\sigma(i)} \]
2 Properties
- Multiplicity: \( det(AB) = det(A)det(B) \)
- Invariant under transposition: \( det(A^T) = det(A) \)