A Cramer rule for finding the solution of a class of singular equations. (English) Zbl 0671.15006

Let A be an \(n\times n\) complex matrix and let k be the least nonnegative integer such that rank \(A^ k=rank A^{k+1}\). If b is in the range of \(A^ k\), then there is a unique x in the range of \(A^ k\) such that \(Ax=b\). The author obtains a Cramer’s rule type result for finding this solution. The result reduces to the usual Cramer’s rule for nonsingular A.
Reviewer: G.P.Barker


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