The inverse of a matrix A in linear algebra is the matrix A-1, which, when multiplied with the original matrix, is equal to the identity matrix I. This can be written as follows:
A A-1 = I
The inv() function in the numpy.linalg package can invert an example matrix with the following steps:
Create the example matrix with the
mat()function we used in the previous chapters:A = np.mat("0 1 2;1 0 3;4 -3 8") print("A\n", A)The
Amatrix appears as follows:A [[ 0 1 2] [ 1 0 3] [ 4 -3 8]]
Invert the matrix with the
inv()function:inverse = np.linalg.inv(A) print("inverse of A\n", inverse)The inverse matrix appears as follows:
inverse of A [[-4.5 7. -1.5] [-2. 4. -1. ] [ 1.5 -2. 0.5]]
Check the result by multiplying the original matrix with the result of the
inv()function...