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fzmultPurposeSyntaxMultiplication with fundamental nullspace basisW = fzmult(A,V)W = fzmult(A,V,'transpose')[W,L,U,pcol,P] = fzmult(A,V)W = fzmult(A,V,transpose,L,U,pcol,P)Description W = fzmult(A,V) computes the product W of matrix Z with matrix V,that is, W = Z*V,whereZ is a fundamental basis for the nullspace ofmatrix A. A must be a sparse m-by-n matrix where m < n, rank(A) = m,and rank(A(1:m,1:m)) = m. V must be p-by-q, wherep = n-m. IfV issparse W is sparse, else W is full.W = fzmult(A,V,'transpose') computes the product of the transposeof the fundamental basis times V, thatis,W = Z'*V. V must be p-by-q,where q = n-m. fzmult(A,V) isthesameasfzmult(A,V,[]).[W,L,U,pcol,P] = fzmult(A,V) returns the sparse LU-factorizationof matrix A(1:m,1:m), thatis,A1 = A(1:m,1:m) andP*A1(:,pcol) = L*U.W = fzmult(A,V,transpose,L,U,pcol,P) uses the precomputedsparse LU factorization of matrix A(1:m,1:m),thatis,A1 = A(1:m,1:m)and P*A1(:,pcol) = L*U. transpose is either 'transpose' or [].The nullspace basis matrix Z is not formed explicitly. An implicitrepresentation is used based on the sparse LU factorization ofA(1:m,1:m).8-129