Solve AX=B for X when A is square matrix
The LU Solver block solves the linear system AX=B by applying LU factorization to the M-by-M matrix at the A port. The input to the B port is the right side M-by-N matrix, B. The M-by-N matrix output X is the unique solution of the equations.
The block treats length-M unoriented vector input to the input port B as an M-by-1 matrix.
The LU algorithm factors a row-permuted variant (Ap) of the square input matrix A as
where L is a lower triangular square matrix with unity diagonal elements, and U is an upper triangular square matrix.
The matrix factors are substituted for Ap in
where Bp is the row-permuted variant of B, and the resulting equation
is solved for X by making the substitution Y = UX, and solving two triangular systems.
See Solve AX=B Using the LU Solver Block in the DSP System Toolbox™ User's Guide.