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Books on the topic 'Generalized Matrix Inverse (or g-inverse)'

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Published: 5 June 2025

Last updated: 24 June 2025

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1

Xiaowen, Fang, and United States. National Aeronautics and Space Administration., eds. Optimal control of large space structures via generalized inverse matrix. Dept. of Electrical Engineering, Catholic University of America, 1988.

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2

Kei, Takeuchi, Takane Yoshio, and SpringerLink (Online service), eds. Projection Matrices, Generalized Inverse Matrices, and Singular Value Decomposition. Springer Science+Business Media, LLC, 2011.

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3

Campbell, S. L. Generalized inverses of linear transformations. Society for Industrial and Applied Mathematics, 2009.

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4

Campbell, S. L. Generalized inverses of linear transformations. Dover Publications, 1991.

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5

Bapat, Ravindra B., Steve J. Kirkland, K. Manjunatha Prasad, and Simo Puntanen, eds. Combinatorial Matrix Theory and Generalized Inverses of Matrices. Springer India, 2013. http://dx.doi.org/10.1007/978-81-322-1053-5.

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6

Bapat, Ravindra B. Combinatorial Matrix Theory and Generalized Inverses of Matrices. Springer India, 2013.

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7

Hazra, A. K. Matrix: Algebra, Calculus and Generalized Inverse. Cambridge International Science Publishing, 2006.

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8

Pringle, R. M., A. A. Rayner, and Alan Stuart. Generalized Inverse Matrices with Applications to Statistics. Hafner Press, 1986.

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9

Hazra, A. K. Matrix: Algebra, Calculus and Generalized Inverse (Part II). Cambridge International Science Publishing, 2007.

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10

Takeuchi, Kei, Haruo Yanai, and Yoshio Takane. Projection Matrices, Generalized Inverse Matrices, and Singular Value Decomposition. Springer, 2011.

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11

Takeuchi, Kei, Haruo Yanai, and Yoshio Takane. Projection Matrices, Generalized Inverse Matrices, and Singular Value Decomposition. Springer New York, 2013.

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12

Cheng, Russell. Examples of Embedded Distributions. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198505044.003.0006.

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This chapter gives examples of probability distributions that, in their conventional parametrization, contain embedded models. Embeddedness is not intrinsic but depends on the parametrization. The simplest way to reveal and remove embeddedness is to reparametrize and make the log-likelihood, L, expandable as a Maclaurin series of one parameter, α‎: L = L0 + L1α‎ + L2α‎2 + … with L0 the log-likelihood of the embedded model hidden in the original parametrization. The quantity L1, rescaled using the information matrix, is the score statistic which can be used for formally comparing the original and embedded model fits. Embeddedness occurs in many distributions if there is a shifted threshold parameter. Examples given in the chapter are the Burr XII, gamma, generalized extreme value, inverse Gaussian, inverted gamma, logistic, loglogistic, lognormal, loggamma, Pareto, and Weibull distributions. Another interesting example occurs in early parametrizations of the stable law distribution.

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13

Ben-Israel, Adi, and Thomas N. E. Greville. Generalized Inverses: Theory and Applications. Springer London, Limited, 2006.

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14

Ben-Israel, Adi. Generalized Inverses: Theory And Applications. Springer, 2010.

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15

Ivan Stanimirović. Computation of Generalized Matrix Inverses and Applications. Apple Academic Press, Incorporated, 2017.

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16

Stanimirovic, Ivan. Computation of Generalized Matrix Inverses and Applications. Taylor & Francis Group, 2021.

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17

Computation of Generalized Matrix Inverses and Applications. Apple Academic Press, Incorporated, 2017.

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18

K. P. S. Bhaskara Rao. Theory of Generalized Inverses over Commutative Rings. Taylor & Francis Group, 2002.

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19

K. P. S. Bhaskara Rao. Theory of Generalized Inverses over Commutative Rings. Taylor & Francis Group, 2002.

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20

K. P. S. Bhaskara Rao. Theory of Generalized Inverses over Commutative Rings. Taylor & Francis Group, 2002.

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21

K. P. S. Bhaskara Rao. Theory of Generalized Inverses over Commutative Rings. Taylor & Francis Group, 2002.

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22

K. P. S. Bhaskara Rao. Theory of Generalized Inverses over Commutative Rings. Taylor & Francis Group, 2002.

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23

Odell, P. L., and Robert Piziak. Matrix Theory: From Generalized Inverses to Jordan Form. Taylor & Francis Group, 2007.

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24

Odell, P. L., and Robert Piziak. Matrix Theory: From Generalized Inverses to Jordan Form. Taylor & Francis Group, 2007.

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25

Kirkland, Stephen James, Simo Puntanen, Ravindra B. Bapat, and K. Manjunatha Prasad. Combinatorial Matrix Theory and Generalized Inverses of Matrices. Ingramcontent, 2015.

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26

Combinatorial Matrix Theory and Generalized Inverses of Matrices. Springer, 2013.

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27

Theory of Generalized Inverses Over Commutative Rings. CRC Press, 2002.

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28

Numerical And Symbolic Computations Of Generalized Inverses. WSPC, 2018.

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29

Matrix Theory: From Generalized Inverses to Jordan Form (Pure and Applied Mathematics). Chapman & Hall/CRC, 2007.

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