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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.