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    %% Rank, Column Space, and Null Space of Matrix
% Use the results of the singular value decomposition to determine the
% rank, column space, and null space of a matrix.
A = [2 0 2; 0 1 0; 0 0 0]

%%
[U,S,V] = svd(A)

%%
% Calculate the rank using the number of nonzero singular values.
s = diag(S);
rank_A = nnz(s)

%%
% Compute an orthonormal basis for the column space of |A| using the
% columns of |U| that correspond to nonzero singular values.
column_basis = U(:,logical(s))

%%
% Compute an orthonormal basis for the null space of |A| using the columns
% of |V| that correspond to singular values equal to zero.
null_basis = V(:,~s)

%%
% The functions |rank|, |orth|, and |null| provide convenient ways to
% calculate these quantities.