Drazin inverse

Drazin inverse

Differential Equations and Stability

Published in Leslie Hogben, Richard Brualdi, Anne Greenbaum, Roy Mathias, Handbook of Linear Algebra, 2006

A Drazin inverseAD of a matrix A ∈ ℂn×n is defined as the unique solution of the system of matrix equations ADAAD=AD,AAD=ADA,Ak+1AD=Ak,

Varying-parameter Zhang neural network for approximating some expressions involving outer inverses

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Journal Information

Published in Optimization Methods and Software, 2020

Predrag S. Stanimirović, Vasilios N. Katsikis, Zhijun Zhang, Shuai Li, Jianlong Chen, Mengmeng Zhou

As mentioned, the Moore–Penrose inverse, the Drazin inverse and several another dominant generalized inverses are outer inverses with prescribed range and null space. The general zeroing design which comprises all previously defined models was originated in [37] and it is aimed to computation of -inverses of time-varying complex matrices. The research in [37] was motivated by this fact. The ZNNATS2-I model defined in [37] was defined using the input matrix and an appropriate matrix , . After the choice of , ZNNATS2-I is aimed to the computation of . The ZNNATS2-I design is defined starting from the identities and , which implies two dual Zhang functions, proposed in [37]:

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Differential Equations and Stability

Varying-parameter Zhang neural network for approximating some expressions involving outer inverses