Normalizing columns of a matrix

Question

Muzammil Behzad 2016-4-22

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https://ww2.mathworks.cn/matlabcentral/answers/280464-normalizing-columns-of-a-matrix

回答： Julia Gala 2017-12-4

Hello everyone,

I have a matrix of, let's say 10000x10000 size, and I want to normalize each column of the matrix by its respective norm (let's say ith column divided norm of ith column) and also store the respective norms in another vector (so there'll be a vector of size 10000x1 where each row will correspond to norm of respective column). This is of course achievable by using a for loop but I need to know if there's any optimum way or a function that would do it for me quickly.

Thanks.

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Answer 1

Roger Stafford 2016-4-22

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Assume by "norm" you mean the usual 2-norm, and that your 10000 x 10000 matrix is named 'M'.

   n = sqrt(sum(M.^2,1)); % Compute norms of columns
   M = bsxfun(@rdivide,M,n); % Normalize M
   n = reshape(n,[],1); % Store column vector of norms