You are given an integer matrix of size N * M (a matrix is a 2D array of numbers).
A norm is a positive value meant to quantify the "size/length" of an element. In our case we want to compute the norm of a matrix.
There exist several norms, used for different scenarios.
Some of the most common matrix norms are :
- The norm 1: for each column of the matrix, compute the sum of the absolute values of every element in that column. The norm 1 is the maximum of these sums.
- The infinite norm: for each row of the matrix, compute the sum of the absolute values of every element in that row. The infinite norm is the maximum of these sums.
- The max norm: compute the maximum of the absolute values of every element in the matrix.
Given the matrix, print these three norms.