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A representation of the minimal \(P\)-norm solution. (English) Zbl 1005.15001

By using the determinantal representation and conditions for the existence of the Drazin inverse from the paper of P. S. Stanimirović and D. S. Djordjević [Linear Algebra Appl. 311, No. 1-3, 131-151 (2000; Zbl 0956.15005)], the author introduces a determinantal representation of the minimal \(P\)-norm solution of a given linear system. More precisely, he represents elements of the minimal \(P\)-norm solution \(A^Db\) as fractions of two expressions involving minors of the order \(\operatorname{rank}(A^k)\), \(k=\operatorname{ind}(A)\), taken from the matrix \(A\) and from its rank invariant powers \(A^l\), \(l\geq k\).

MSC:

15A09 Theory of matrix inversion and generalized inverses

Citations:

Zbl 0956.15005
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