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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

MSC:

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

[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
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