Norm generally refers to the norm of three options: 1-norm, 2-norm, and inf-norm, corresponding to the MATLAB command norm(A, p)
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The 1-norm of a vector is the sum of the absolute values of each element of the vector, corresponding to sum(abs(X))
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The 1-norm of the matrix is the maximum value of the 1-norm of each column vector col of the matrix, corresponding to max(sum(abs(X)))
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The 2-norm of a vector is also called the Euclidean norm. It is the module of the vector that we are familiar with, that is, the length of the vector. It is the square root of the sum of the squares of each element, corresponding to sum(abs(X)^2)^(1 /2)
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The 2-norm of the matrix is the largest svd singular value of the matrix, corresponding to max(svd(X))
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The inf-norm of a vector is the maximum absolute value of each element of the vector, corresponding to max(abs(X))
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The inf-norm of the matrix is the maximum value of the 1-norm of each row vector row of the matrix, corresponding to max(sum(abs(X')))
Replenish:
- The frobenius-norm of a matrix is the square root of the sum of the squares of each element of the matrix