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1

Matrices and matroids for systems analysis. Springer, 2010.

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2

Murota, Kazuo. Matrices and Matroids for Systems Analysis. Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-03994-2.

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3

R, Johnson Charles, ed. Topics in matrix analysis. Cambridge University Press, 1991.

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4

Marcus, Marvin. A survey of matrix theory and matrix inequalities. Dover, 1992.

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5

Alice, Guionnet, and Zeitouni Ofer, eds. An introduction to random matrices. Cambridge University Press, 2010.

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6

Computational oriented matroids: Equivalence classes of matrices within a natural framework. Cambridge University Press, 2006.

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7

R, Johnson Charles, ed. Matrix analysis. Cambridge University Press, 1985.

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8

Horn, Roger A. Matrix analysis. Cambridge University Press, 1990.

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9

Greville, T. N. E. 1910-, ed. Generalized inverses: Theory and applications. 2nd ed. Springer, 2003.

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10

Jameson, Leland. On the spline-based wavelet differentiation matrix [microform]. National Aeronautics and Space Administration, Langley Research Center, 1993.

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11

Jameson, Leland. On the differentiation matrix for Daubechies-based wavelets on an interval. Institute for Computer Applications in Science and Engineering, 1993.

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12

Jameson, Leland. On the Daubechies-based wavelet differentiation matrix. Institute for Computer Applications in Science and Engineering, 1993.

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13

F, Van Loan Charles, ed. Matrix computations. 3rd ed. Johns Hopkins University Press, 1996.

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14

Jameson, Leland. On the spline-based wavelet differentiation matrix [microform]. National Aeronautics and Space Administration, Langley Research Center, 1993.

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15

Jameson, Leland. On the spline-based wavelet differentiation matrix [microform]. National Aeronautics and Space Administration, Langley Research Center, 1993.

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16

Jameson, Leland. On the spline-based wavelet differentiation matrix. Institute for Computer Applications in Science and Engineering, 1993.

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17

Golub, Gene H. Matrix computations. 2nd ed. Johns Hopkins University Press, 1989.

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18

Lange, Jan de. Matrices. Wings for Learning, 1992.

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19

Matrices. Acer Press, 2007.

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20

Serre, Denis. Matrices. Springer New York, 2010. http://dx.doi.org/10.1007/978-1-4419-7683-3.

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21

Norton, Pam. Matrices. Edited by Leigh-Lancaster David and Australian Council for Educational Research. ACER Press, 2007.

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22

Hadamard matrices and their applications. Springer-Verlag, 1985.

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23

Matrix theory: A second course. Plenum Press, 1987.

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24

Thomas, King J., ed. Matrix methods andapplications. Prentice Hall, 1988.

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25

Groetsch, C. W. Matrix methods and applications. Prentice Hall, 1988.

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26

Dellacherie, Claude, Servet Martinez, and Jaime San Martin. Inverse M-Matrices and Ultrametric Matrices. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-10298-6.

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27

Fujishige, Satoru. Matroids on convex geometries (cg-matroids). Research Institute for Mathematical Sciences, Kyoto University, 2006.

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28

Dziedzic, Stanislaw. Swiety szlak Almae Matris. Wydawnictwo WAM, 2003.

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29

Dziedzic, Stanisław. Święty szlak Almae Matris. Wydawn. WAM, 2003.

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30

Matria. Editorial Cuarto Propio, 2007.

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31

Nonnegative matrices. Wiley, 1988.

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32

Random matrices. 3rd ed. Elsevier/Academic Press, 2004.

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33

Random matrices. 2nd ed. Academic Press, 1991.

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34

Minc, Henryk. Nonnegative matrices. Wiley, 1988.

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35

Nicolaides, A. Determinants & matrices. Private Academic & Scientific Studies, 1994.

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36

Borovik, Alexandre V. Coxeter Matroids. Birkhäuser Boston, 2003.

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37

Lange, Jan de. Grafen & matrices. Wiskunde A, 1988.

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38

Mehta, Madan Lal. Random matrices. 2nd ed. Academic Press, 1991.

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39

Krylov, Piotr, and Askar Tuganbaev. Formal Matrices. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-53907-2.

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40

Borovik, Alexandre V., I. M. Gelfand, and Neil White. Coxeter Matroids. Birkhäuser Boston, 2003. http://dx.doi.org/10.1007/978-1-4612-2066-4.

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41

Borodin, Alexei, Ivan Corwin, and Alice Guionnet, eds. Random Matrices. American Mathematical Society, 2019. http://dx.doi.org/10.1090/pcms/026.

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42

V, Ramaswami, ed. Introduction to matrix analytic methods in stochastic modeling. Society for Industrial and Applied Mathematics, 1999.

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43

Applied linear algebra and matrix analysis. Springer, 2006.

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44

Murota, Kazuo. Matrices and Matroids for Systems Analysis. Springer, 2010.

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45

Matrix Theory. World Scientific Publishing Company, 1991.

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46

Matrix Theory. World Scientific Publishing Company, 1991.

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47

Lewis, David W. Matrix Theory. Allied Publishers Pvt. Ltd., 1995.

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48

Murota, Kazuo. Matrices and Matroids for Systems Analysis (Algorithms and Combinatorics). Springer, 2000.

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49

Bokowski, Juergen G. Computational Oriented Matroids: Equivalence Classes of Matrices within a Natural Framework. Cambridge University Press, 2006.

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50

Bertola, Marco. Chain of matrices, loop equations, and topological recursion. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.16.

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Abstract:
This article considers the so-called loop equations satisfied by integrals over random matrices coupled in a chain as well as their recursive solution in the perturbative case when the matrices are Hermitian. Random matrices are used in fields such as the study of multi-orthogonal polynomials or the enumeration of discrete surfaces, both of which are based on the analysis of a matrix integral. However, this term can be confusing since the definition of a matrix integral in these two applications is not the same. The article discusses these two definitions, perturbative and non-perturbative, al
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