A Cramer rule for minimum-norm (T) least-squares (S) solution of inconsistent linear equations. (English) Zbl 0588.15005

The author gives the minimum norm (T) least-squares (S) solution of inconsistent linear equations \(Ax=y\) in terms of determinants. This solution is reduced to Cramer’s rule when A is non-singular.
Reviewer: P.Narain


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


[1] Robinson, S. M.; Montgomery, S., Selected Papers on Algebra, Math. Assoc. Amer., 313-314 (1977), reprinted in
[2] Ben-Israel, A., A Cramer rule for least-norm solution of consistent linear equations, Linear Algebra Appl., 43, 223 (1982) · Zbl 0487.15004
[3] Verghese, G. C., A “Cramer rule” for least-norm least-square-error solution of inconsistent linear equations, Linear Algebra Appl., 48, 315 (1982) · Zbl 0501.15004
[4] Ben-Israel, A.; Greville, T. N.E., Generalized Inverses: Theory and Applications (1974), Wiley-Interscience · Zbl 0305.15001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.