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A GENERALIZATION OF MATRIX INVERSION WITH APPLICATION TO LINEAR DIFFERENTIAL-ALGEBRAIC

A new generalized inversion for square matrices based on projections is introduced. It includes as special cases known generalized inverses such as the Moore-Penrose and the Drazin inverses. When associated with a regular matrix pencil, it can be expressed by a contour integral formula and can be used, in particular, to write down an explicit representation of the solutions of linear differential algebraic systems. The representation can further be simplified when a well chosen expansion is used for the exponential function. An illustration is given with the expansion in Laguerre functions.