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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 = rank. The Drazin inverse of A is the unique matrix A which satisfies
It's not a generalized inverse in the classical sense, since A A D A ≠ A {\displaystyle AA^{\text{D}}A\neq A} in general.
The hyper-power sequence is
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