Determinants and matrix operations:
- $\det(AB) = \det(A)\det(B)$
- $\det(A^T) = \det(A)$
- $\det(cA) = c^n \det(A)$ for $n \times n$ matrix
- $\det(A^{-1}) = 1/\det(A)$
- Row swap changes sign of determinant
- Row scaling by $c$ multiplies determinant by $c$
- Row replacement does not change determinant
Parents
Children
- Definition of determinant of a matrix as a product of the diagonal entries in a non-scaled echelon form.
- The determinant of a matrix can be expressed as a product of the diagonal entries in a non-scaled echelon form.
- Definition of the determinant in terms of the effect of elementary row operations
- The permutation expansion for determinants
- A matrix and its transpose have the same determinant.
- If A and B are n-by-n matrices
- The determinant of the inverse of A is the reciprocal of the determinant of A.
- The determinant of a block diagonal matrix is the product of the determinants of the blocks.