Geometry of matrix decomposition

Ke Ye
University of Chicago

The matrix decomposition problem (MDP) concerns the possibility and feasibility of decomposing an arbitrary (generic) matrix into the product of matrices of a given type. For instance, LU, QR and SVD decompositions are well known examples of the MDP. The most important goal of the MDP is to find a better algorithm to solve a linear system. I will introduce the method of applying algebraic geometry to solve the MDP. I will first derive some general results using algebraic geometry and then apply them to some specific examples.

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