What is the Frobenius norm of a matrix?
Let’s say A is an mxn matrix. The Frobenius norm of the matrix A is defined as:
Here, Ai,j is the element in the ith row and jth column of the matrix A. In other words, if we take all the elements of the matrix, square them and sum them up and then, take the square root of the result, we will get the Frobenius norm of the matrix.
Let’s look at an example. Let’s say, A is the following matrix:
So, the Frobenius norm of the matrix A will be:
How to calculate the Frobenius norm of a matrix using Python?
We can use the following Python code to calculate the Frobenius norm of a matrix.
import numpy from numpy.linalg import norm A = numpy.array([[1, 2], [3, 4]]) F_norm = norm(A, ord="fro") print("Matrix A: \n", A) print("The Frobenius norm of the matrix A: ", F_norm)
Here, A is a matrix. We are using the norm() function from numpy.linalg to calculate the Frobenius norm of the matrix. The argument ord=”fro” specifies that we want to calculate the Frobenius norm.
The output of the mentioned program will be:
Matrix A: [[1 2] [3 4]] The Frobenius norm of the matrix A: 5.477225575051661






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