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- W2084609682 abstract "Let A, B be $n times n$ complex matrices and assume $(A + lambda B)^{ - 1} $ exists for some complex number $lambda $; then $(A + lambda B)^{ - 1} $ has a Laurent expansion of the form $sum_{k = - nu }^infty {Q_k lambda ^k } $ with $Q_{ - nu } ne 0$ valid in some deleted neighborhood of $lambda = 0$. Explicit formulas for the $Q_k $ are given. Expansions of powers of $(A + lambda B)^{ - 1} A$ are also given. The expansions are used to obtain various characterizations of the Drazin inverse and other inverses as limits. Finally the expansions, together with Laplace transforms, are used to solve the differential equations $Adot x + Bx = 0$ and $Addot x + Bx = 0$, where A may be singular, in the case when unique solutions exist for appropriate initial conditions." @default.
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- W2084609682 date "1978-08-01" @default.
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- W2084609682 title "The Laurent Expansion of a Generalized Resolvent with Some Applications" @default.
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- W2084609682 doi "https://doi.org/10.1137/0509054" @default.
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