Drazin inverse
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In mathematics, the Drazin inverse, named after Michael P. Drazin, is a kind of generalized inverse of a matrix.
Let A be a square matrix. The index of A is the least nonnegative integer k such that rank(Ak+1)=rank(Ak). The Drazin inverse of A is the unique matrix X, which satisfies
The Drazin inverse of a matrix of index 1 is called the group inverse.
[edit] References
- Drazin, M. P., Pseudo-inverses in associative rings and semigroups, The American Mathematical Monthly 65(1958)506-514 JSTOR
- Bing Zheng and R. B. Bapat, Generalized inverse A(2)T,S and a rank equation, Applied Mathematics and Computation 155 (2004) 407-415 DOI 10.1016/S0096-3003(03)00786-0