“Moore-Penrose Generalized Matrix Inverse”的概念、定义、习题解题方法及翻译-数学辞典

单词

Moore-Penrose Generalized Matrix Inverse

释义

Moore-Penrose Generalized Matrix Inverse

Given an Matrix , the Moore-Penrose generalized Matrix Inverse is a unique Matrix which satisfies

It is also true that

(5)

is the shortest length Least Squares solution to the problem

(6)

If the inverse of exists, then

(7)

where

is the Matrix Transpose, as can be seen by premultiplying both sides of (7) by

to create a Square Matrix which can then be inverted,

(8)

giving


			(9)

See also Least Squares Fitting, Matrix Inverse

References

Ben-Israel, A. and Greville, T. N. E. Generalized Inverses: Theory and Applications. New York: Wiley, 1977.

Lawson, C. and Hanson, R. Solving Least Squares Problems. Englewood Cliffs, NJ: Prentice-Hall, 1974.

Penrose, R. ``A Generalized Inverse for Matrices.'' Proc. Cambridge Phil. Soc. 51, 406-413, 1955.

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