Vector norm of an array of vectors in MATLAB

arrays, matlab, matrix, normalization, vectorization

Solution

You can compute the norm of each column or row of a matrix yourself by using element-wise arithmetic operators and functions defined to operate over given matrix dimensions (like SUM and MAX). Here's how you could compute some column-wise norms for a matrix `M`:

twoNorm = sqrt(sum(abs(M).^2,1)); %# The two-norm of each column
pNorm = sum(abs(M).^p,1).^(1/p);  %# The p-norm of each column (define p first)
infNorm = max(M,[],1);            %# The infinity norm (max value) of each column

These norms can easily be made to operate on the rows instead of the columns by changing the dimension arguments from `...,1` to `...,2`.

Problem

When calling `norm` on a matrix in MATLAB, it returns what's known as a "matrix norm" (a scalar value), instead of an array of vector norms. Is there any way to obtain the norm of each vector in a matrix without looping and taking advantage of MATLAB's vectorization?

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