Abstract
A mapping φ:R n→R m, n≤m, with Jacobian of full column-rank, has a local inverse that is analogous to the Moore–Penrose inverse of linear mappings.
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References
R.B. Bapat and A. Ben-Israel, Singular values and maximum rank minors of generalized inverses, Linear and Multilinear Algebra 40 (1995) 153–161.
A. Ben-Israel, A volume associated with m × n matrices, Linear Algebra Appl. 167 (1992) 87–111.
A. Ben-Israel, The change of variables formula using matrix volume, SIAM J. Matrix Anal. 21 (1999) 300–312.
A. Ben-Tal and M. Teboulle, A geometric property of the least squares solution of linear equations, Linear Algebra Appl. 139 (1990) 165–170.
L. Berg, Three results in connection with inverse matrices, Linear Algebra Appl. 84 (1986) 63–77.
L.H. Loomis and S. Sternberg, Advanced Calculus (Addison-Wesley, Reading, MA, 1968).
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Ben-Israel, A. A local inverse for nonlinear mappings. Numerical Algorithms 25, 37–46 (2000). https://doi.org/10.1023/A:1016698101320
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DOI: https://doi.org/10.1023/A:1016698101320