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On extensions of Cramer’s rule for solutions of restricted linear systems. (English) Zbl 0544.15002

The author extends a method of Ben-Israel (which derives a Cramer rule for the minimum Euclidean-norm solution of a consistent linear equation) such that it becomes possible to give the unique solution of a more general consistent restricted linear system a (correspondingly modified) determinantal form. He also introduces a different approach which results in a second and more condensed Cramer rule for the solutions of the considered problem. Moreover, he presents a determinantal formula for any \(\{\) 1,2\(\}\)-generalized inverse of an \(m\times n\) matrix A, which in the case where A is nonsingular reduces to the formula \(A^{-1}=(\det A)^{-1}adj A\); here, the symbol adj A is used to denote the adjoint matrix of A.
Reviewer: N.I.Osetinski

MSC:

15A06 Linear equations (linear algebraic aspects)
15A09 Theory of matrix inversion and generalized inverses
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References:

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