Numpy Linear Algebra

This note covers the numpy.linalg module.

For the mathematics behind these functions, check Linear Algebra.

det() function

Calculates the determinant of a given matrix. The matrix must be a square matrix (n*n).

from numpy import linalg as LA
 
A = np.arrange(1,5).reshape(2,2)
> [[1  2]
   [3 4]]
 
LA.det(A)
> -2

inv() function

Calculates the inverse of a given matrix. The determinant must not be 0 and matrix must be square.

LA.inv(A)
> [[-2     1]
   [1.5 -0.5]]

norm() function

Calculates the norm of a vector. This operation does not work with matrices.

By default, it calculates the L2 norm.

x = np.array([1,2,3,4])
 
LA.norm(x)
> 5.48

By specifying the ord argument, it corresponds to the Lp norm.

LA.norm(x, ord=1)
> 10

When ord is set to np.inf, it calculates the L∞ norm.

LA.norm(x, ord=np.inf)
> 4

L1, L2 and L∞ norms are the most used ones, and they correspond, respectively, to:

• The sum of the absolute values, called Manhattan Norm
• Distance in a straight line in space, called Euclidean Norm
• Biggest absolute value, called L∞ or L_inf