ムーア・ペンローズ逆行列 (Japanese Wikipedia)

Analysis of information sources in references of the Wikipedia article "ムーア・ペンローズ逆行列" in Japanese language version.

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14doi.org

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5harvard.edu

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5jstor.org

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2worldcat.org

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1projecteuclid.org

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1archive.org

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1siam.org

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1sanu.ac.rs

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1uwlax.edu

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1benisrael.net

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1emtiyaz.github.io

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1ethz.ch

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1julialang.org

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1arxiv.org

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archive.org

Golub, Gene H.; Charles F. Van Loan (1996). Matrix computations (3rd ed.). Baltimore: Johns Hopkins. pp. 257–258. ISBN 978-0-8018-5414-9

arxiv.org

Tian, Yongge. "Matrix Theory over the Complex Quaternion Algebra". arXiv:math/0004005。

benisrael.net

Ben-Israel, Adi; Cohen, Dan (1966). “On Iterative Computation of Generalized Inverses and Associated Projections”. SIAM Journal on Numerical Analysis 3 (3): 410–19. Bibcode: 1966SJNA....3..410B. doi:10.1137/0703035. JSTOR 2949637. pdf

doi.org

Moore, E. H. (1920). “On the reciprocal of the general algebraic matrix”. Bulletin of the American Mathematical Society 26 (9): 394–95. doi:10.1090/S0002-9904-1920-03322-7.
Penrose, Roger (1955). “A generalized inverse for matrices”. Proceedings of the Cambridge Philosophical Society 51 (3): 406–13. Bibcode: 1955PCPS...51..406P. doi:10.1017/S0305004100030401.
Greville, T. N. E. (1966-10-01). “Note on the Generalized Inverse of a Matrix Product”. SIAM Review 8 (4): 518–521. doi:10.1137/1008107. ISSN 0036-1445.
Maciejewski, Anthony A.; Klein, Charles A. (1985). “Obstacle Avoidance for Kinematically Redundant Manipulators in Dynamically Varying Environments”. International Journal of Robotics Research 4 (3): 109–117. doi:10.1177/027836498500400308.
Golub, G. H.; Pereyra, V. (April 1973). “The Differentiation of Pseudo-Inverses and Nonlinear Least Squares Problems Whose Variables Separate”. SIAM Journal on Numerical Analysis 10 (2): 413–32. Bibcode: 1973SJNA...10..413G. doi:10.1137/0710036. JSTOR 2156365.
Stallings, W. T.; Boullion, T. L. (1972). “The Pseudoinverse of an r-Circulant Matrix”. Proceedings of the American Mathematical Society 34 (2): 385–88. doi:10.2307/2038377. JSTOR 2038377.
Ben-Israel, Adi; Cohen, Dan (1966). “On Iterative Computation of Generalized Inverses and Associated Projections”. SIAM Journal on Numerical Analysis 3 (3): 410–19. Bibcode: 1966SJNA....3..410B. doi:10.1137/0703035. JSTOR 2949637. pdf
Söderström, Torsten; Stewart, G. W. (1974). “On the Numerical Properties of an Iterative Method for Computing the Moore–Penrose Generalized Inverse”. SIAM Journal on Numerical Analysis 11 (1): 61–74. Bibcode: 1974SJNA...11...61S. doi:10.1137/0711008. JSTOR 2156431.
Meyer, Jr., Carl D. (1973). “Generalized inverses and ranks of block matrices”. SIAM J. Appl. Math. 25 (4): 597–602. doi:10.1137/0125057.
Meyer, Jr., Carl D. (1973). “Generalized inversion of modified matrices”. SIAM J. Appl. Math. 24 (3): 315–23. doi:10.1137/0124033.
Penrose, Roger (1956). “On best approximate solution of linear matrix equations”. Proceedings of the Cambridge Philosophical Society 52 (1): 17–19. Bibcode: 1956PCPS...52...17P. doi:10.1017/S0305004100030929.
Planitz, M. (October 1979). “Inconsistent systems of linear equations”. Mathematical Gazette 63 (425): 181–85. doi:10.2307/3617890. JSTOR 3617890.
James, M. (June 1978). “The generalised inverse”. Mathematical Gazette 62 (420): 109–14. doi:10.1017/S0025557200086460.
Pearl, Martin H. (1968-10-01). “Generalized inverses of matrices with entries taken from an arbitrary field” (英語). Linear Algebra and Its Applications 1 (4): 571–587. doi:10.1016/0024-3795(68)90028-1. ISSN 0024-3795.

emtiyaz.github.io

Emtiyaz, Mohammad (February 27, 2008). Updating Inverse of a Matrix When a Column is Added/Removed.

ethz.ch

stat.ethz.ch

“R: Generalized Inverse of a Matrix”. 2022年4月10日閲覧。

harvard.edu

ui.adsabs.harvard.edu

Penrose, Roger (1955). “A generalized inverse for matrices”. Proceedings of the Cambridge Philosophical Society 51 (3): 406–13. Bibcode: 1955PCPS...51..406P. doi:10.1017/S0305004100030401.
Golub, G. H.; Pereyra, V. (April 1973). “The Differentiation of Pseudo-Inverses and Nonlinear Least Squares Problems Whose Variables Separate”. SIAM Journal on Numerical Analysis 10 (2): 413–32. Bibcode: 1973SJNA...10..413G. doi:10.1137/0710036. JSTOR 2156365.
Ben-Israel, Adi; Cohen, Dan (1966). “On Iterative Computation of Generalized Inverses and Associated Projections”. SIAM Journal on Numerical Analysis 3 (3): 410–19. Bibcode: 1966SJNA....3..410B. doi:10.1137/0703035. JSTOR 2949637. pdf
Söderström, Torsten; Stewart, G. W. (1974). “On the Numerical Properties of an Iterative Method for Computing the Moore–Penrose Generalized Inverse”. SIAM Journal on Numerical Analysis 11 (1): 61–74. Bibcode: 1974SJNA...11...61S. doi:10.1137/0711008. JSTOR 2156431.
Penrose, Roger (1956). “On best approximate solution of linear matrix equations”. Proceedings of the Cambridge Philosophical Society 52 (1): 17–19. Bibcode: 1956PCPS...52...17P. doi:10.1017/S0305004100030929.

jstor.org

Golub, G. H.; Pereyra, V. (April 1973). “The Differentiation of Pseudo-Inverses and Nonlinear Least Squares Problems Whose Variables Separate”. SIAM Journal on Numerical Analysis 10 (2): 413–32. Bibcode: 1973SJNA...10..413G. doi:10.1137/0710036. JSTOR 2156365.
Stallings, W. T.; Boullion, T. L. (1972). “The Pseudoinverse of an r-Circulant Matrix”. Proceedings of the American Mathematical Society 34 (2): 385–88. doi:10.2307/2038377. JSTOR 2038377.
Ben-Israel, Adi; Cohen, Dan (1966). “On Iterative Computation of Generalized Inverses and Associated Projections”. SIAM Journal on Numerical Analysis 3 (3): 410–19. Bibcode: 1966SJNA....3..410B. doi:10.1137/0703035. JSTOR 2949637. pdf
Söderström, Torsten; Stewart, G. W. (1974). “On the Numerical Properties of an Iterative Method for Computing the Moore–Penrose Generalized Inverse”. SIAM Journal on Numerical Analysis 11 (1): 61–74. Bibcode: 1974SJNA...11...61S. doi:10.1137/0711008. JSTOR 2156431.
Planitz, M. (October 1979). “Inconsistent systems of linear equations”. Mathematical Gazette 63 (425): 181–85. doi:10.2307/3617890. JSTOR 3617890.