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A Generalized Framework of Linear Multivariable Control by Liansheng Tan

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3

Generalized inverse of matrix and solution of linear system equation

Abstract

This chapter presents a brief introduction to the generalized inverse of matrix, which is needed in the following expositions. This introduction includes the left inverse and right inverse, the Moore-Penrose inverse, the minimization approach to solve an algebraic matrix equation, the full rank decomposition theorem, the least square solution to an algebraic matrix equation, and the singular value decomposition.

Keywords

Generalized inverse of matrix; Left inverse; Right inverse; Moore-Penrose inverse; Full rank decomposition theorem; Least square solution to an algebraic matrix equation; Singular value decomposition

In this chapter, we briefly present some background ...

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