A determinant is a scalar value that is a function of the entries of a square matrix. It arose as a means of determining whether or not a system of equations
import numpy as np
np.linalg.det([[1,3,6], [2,6,4], [2,9,7]])Properties
Desirable properties to construct what’s called “determinant”
- The determinant of an identity matrix is 1
- matrix with rows or columns of zero have determinant of 0
- Swapping rows or columns changes sign
- Behave linearly with rows
- Adding multiples of rows doesn’t change the determinant
Implied properties
The determinant of the inverse matrix is the reciprocal of the determinant.
The determinant of the transpose is equal to the determinant of the matrix
Determinant of a product is the product of determinants
Proof for
matrix
Usage
The matrix has a unique solution only when the determinant is non-zero. It also tells that the matrix is invertible.
If the determinant is 0, the system either has no solution or infinitely many solutions
Calculations
2x2 Matrix
For a
How to derive the formula?
3x3 Matrix
For a
How do we derive the formula?
nxn Matrix
