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A generalized inverse for matrices
Open accessAbstract
This paper describes a generalization of the inverse of a non-singular matrix, as the unique solution of a certain set of equations. This generalized inverse exists for any (possibly rectangular) matrix whatsoever with complex elements. It is used here for solving linear matrix equations, and among other applications for finding an expression for the principal idempotent elements of a matrix. Also a new type of spectral decomposition is given.
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Cited by
Unke, O. T., Chmiela, S., Sauceda, H. E., Gastegger, M., Poltavsky, I., Schütt, K. T., Tkatchenko, A., & Müller, K.-R. (2021) · Chemical Reviews · doi:10.1021/acs.chemrev.0c01111 · Cited by 1,647
Bias between MNI and Talairach coordinates analyzed using the ICBM‐152 brain template
Lancaster, J. L., Tordesillas‐Gutiérrez, D., Martinez, M., Salinas, F., Evans, A., Zilles, K., Mazziotta, J. C., & Fox, P. T. (2007) · Human Brain Mapping · doi:10.1002/hbm.20345 · Cited by 1,464
Numerical Modelling of Instantaneous Plate Tectonics
Minster, J. B., Jordan, T. H., Molnar, P., & Haines, E. (1974) · Geophysical Journal International · doi:10.1111/j.1365-246x.1974.tb00613.x · Cited by 795
Wiggins, R. A. (1972) · Reviews of Geophysics · doi:10.1029/rg010i001p00251 · Cited by 760
Jordan, T. H., & Sverdrup, K. A. (1981) · Bulletin of the Seismological Society of America · doi:10.1785/bssa0710041105 · Cited by 361
Metadata
- Authors
- Penrose, R.
- Venue
- Mathematical Proceedings of the Cambridge Philosophical Society
- Publisher
- Cambridge University Press (CUP)
- Published
- 1955-07
- Volume
- 51
- Issue
- 3
- Pages
- 406-413
- ISSN
- 0305-0041 (ISSN-L)
- 1469-8064
- OpenAlex
- W1974511160
- Cited by
- 4,551
- References
- 0
- FWCI
- 6.39
- Type
- journal article
- Language
- en
- Open access
- bronze
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- Penrose, R. (1955). A generalized inverse for matrices. Mathematical Proceedings of the Cambridge Philosophical Society. https://doi.org/10.1017/s0305004100030401
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