On extensions of Cramer's rule for solutions of restricted linear systems1
- 1 June 1984
- journal article
- research article
- Published by Taylor & Francis in Linear and Multilinear Algebra
- Vol. 15 (3-4) , 319-330
- https://doi.org/10.1080/03081088408817600
Abstract
For the unique solution of a special consistent restricted linear system Ax=bx∊M we derive two different determinantal forms, which both reduce to Cramer's classical rule if A is nonsingular. The representation for the minimum Euclidean-norm solution of Ax=b given recently by Ben-Israel [2] is reobtained in our first approach as special case. A determinantal formula for any {1, 2}-generalized inverse is also given.Keywords
This publication has 6 references indexed in Scilit:
- A Cramer rule for least-norm solutions of consistent linear equationsLinear Algebra and its Applications, 1982
- Penalty Function Methods for the Numerical Solution of Nonlinear Obstacle Problems with Finite ElementsZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1981
- On the matrix monotonicity of generalized inversionLinear Algebra and its Applications, 1979
- A Short Proof of Cramer's RuleMathematics Magazine, 1970
- On Least Squares with Insufficient ObservationsJournal of the American Statistical Association, 1964
- Vector Spaces and MatricesPhysics Today, 1957