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different decompositions can be used to solve the linear problem, depending on the characteristics of the matrix A and the vectors x and b, which may make one factorization much easier to obtain than others. If A = QR is a QR factorization of A, then equivalently . This is as easy to compute as a matrix factorization. If is an eigendecomposition A, and we seek to find b so that b = Ax, with and , then we have . This is closely related to the solution to the linear system using the singular value decomposition, because singular values of a matrix

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