Matrix Inverse

A Matrix has an inverse Iff the Determinant . For a Matrix

(1)

(2)

(3)

The inverse of a Product of Matrices and can be expressedin terms of and . Let

(4)

(5)

(6)

(7)

(8)

(9)

References

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

Nash, J. C. Compact Numerical Methods for Computers: Linear Algebra and Function Minimisation, 2nd ed. Bristol, England: Adam Hilger, pp. 24-26, 1990.

Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. ``Is Matrix Inversion an Process?'' §2.11 in Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press, pp. 95-98, 1992.

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