MAT G=MPINV(A) computes the Moore-Penrose inverse G of any m*n matrix A. If m<n, G is computed as MPINV(A')'. Let the singular value decomposition of A be A=U*D*V' where D is the diagonal matrix of singular values d1>=d2>=,...,>=dm>=0. Then MPINV(A)=V*INV_D*U' where INV_D is a diagonal matrix of numbers ei, i=1,2,...,m where e1=1/di if di>=eps*d1 and e1=0 otherwise. eps is given by a specification EPS. By default eps=1e-15. G is the only generalized inverse of A satisfying the conditions AGA=A, GAG=G, (AG)'=AG, (GA)'=GA. Certain useful MAT expressions (proposed by Simo Puntanen): MAT P=A*MPINV(A) is the orthogonal projector (with respect to standard inner product) onto the column space of A. MAT C=A*MPINV(A'*V*A)*A'*V is the orthogonal projector (with respect to inner product matrix V) onto the column space of A. MAT P=IDN(m,m)-BASIS(A)*(BASIS(A))'. is the orthogonal projector (with respect to standard inner product) onto the orthocomplement of the column space of A. MAT Z=BASIS(IDN(m,m)-BASIS(A)*(BASIS(A))'). is the orthonormal basis of the orthocomplement of the column space of A.

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