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Journal articles on the topic 'Sign pattern matrices'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Eschenbach, Carolyn A., Frank J. Hall, and Zhongshan Li. "Eigenvalue frequency and consistent sign pattern matrices." Czechoslovak Mathematical Journal 44, no. 3 (1994): 461–79. http://dx.doi.org/10.21136/cmj.1994.128471.

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2

Eschenbach, Carolyn A., Frank J. Hall, and Zhongshan Li. "From real to complex sign pattern matrices." Bulletin of the Australian Mathematical Society 57, no. 1 (1998): 159–72. http://dx.doi.org/10.1017/s0004972700031518.

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This paper extends some fundamental concepts of qualitative matrix analysis from sign pattern classes of real matrices to sign pattern classes of complex matrices. A complex sign pattern and its corresponding sign pattern class are defined in such a way that they generalize the definitions of a (real) sign pattern and its corresponding sign pattern class. A survey of several qualitative results on complex sign patterns is presented. In particular, sign nonsingular complex patterns are investigated. The type of region in the complex plane representing the distribution of the determinants of the

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3

Stuart, Jeffrey. "Reducible sign k-potent sign pattern matrices." Linear Algebra and its Applications 294, no. 1-3 (1999): 197–211. http://dx.doi.org/10.1016/s0024-3795(99)00067-1.

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4

Stuart, Jeffrey, Carolyn Eschenbach, and Steve Kirkland. "Irreducible sign k-potent sign pattern matrices." Linear Algebra and its Applications 294, no. 1-3 (1999): 85–92. http://dx.doi.org/10.1016/s0024-3795(99)00076-2.

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5

Araújo, C. Mendes, and Juan R. Torregrosa. "Sign pattern matrices that admit P0-matrices." Linear Algebra and its Applications 435, no. 8 (2011): 2046–53. http://dx.doi.org/10.1016/j.laa.2011.03.066.

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6

Das, Sunil. "Potentially stable and 5-by-5 spectrally arbitrary tree sign pattern matrices with all edges negative." Electronic Journal of Linear Algebra 37 (July 29, 2021): 562–82. http://dx.doi.org/10.13001/ela.2021.5969.

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Characterization of potentially stable sign pattern matrices has been a long-standing open problem. In this paper, we give some sufficient conditions for tree sign pattern matrices with all edges negative to allow a properly signed nest. We also characterize potentially stable star and path sign pattern matrices with all edges negative. We give a conjecture on characterizing potentially stable tree sign pattern matrices with all edges negative in terms of allowing a properly signed nest which is verified to be true for sign pattern matrices up to order 6. Finally, we characterize all 5-by-5 sp

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7

Eschenbach, Carolyn A., and Zhongshan Li. "Potentially nilpotent sign pattern matrices." Linear Algebra and its Applications 299, no. 1-3 (1999): 81–99. http://dx.doi.org/10.1016/s0024-3795(99)00163-9.

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8

Eschenbach, Carolyn. "Idempotence for sign-pattern matrices." Linear Algebra and its Applications 180 (February 1993): 153–65. http://dx.doi.org/10.1016/0024-3795(93)90529-w.

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9

Lee, Sang-Gu, and Jin-Woo Park. "Sign idempotent sign pattern matrices that allow idempotence." Linear Algebra and its Applications 487 (December 2015): 232–41. http://dx.doi.org/10.1016/j.laa.2015.09.020.

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10

Yeh, Lina. "Sign pattern matrices that allow a nilpotent matrix." Bulletin of the Australian Mathematical Society 53, no. 2 (1996): 189–96. http://dx.doi.org/10.1017/s0004972700016907.

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11

Hou, Yaoping, and Jiongsheng Li. "Square nearly nonpositive sign pattern matrices." Linear Algebra and its Applications 327, no. 1-3 (2001): 41–51. http://dx.doi.org/10.1016/s0024-3795(00)00318-9.

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12

Hall, Frank J., Zhongshan Li, and Bhaskara Rao. "From Boolean to sign pattern matrices." Linear Algebra and its Applications 393 (December 2004): 233–51. http://dx.doi.org/10.1016/j.laa.2004.08.005.

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13

Johansson, Robert, and Svante Linusson. "Pattern Avoidance in Alternating Sign Matrices." Annals of Combinatorics 11, no. 3-4 (2007): 471–80. http://dx.doi.org/10.1007/s00026-007-0330-1.

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14

Waters, Charles. "Sign pattern matrices that allow orthogonality." Linear Algebra and its Applications 235 (March 1996): 1–13. http://dx.doi.org/10.1016/0024-3795(94)00098-0.

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15

Eschenbach, Carolyn A., Frank J. Hall, and Zhongshan Li. "Sign pattern matrices and generalized inverses." Linear Algebra and its Applications 211 (November 1994): 53–66. http://dx.doi.org/10.1016/0024-3795(94)90082-5.

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16

Shao, Yanling, Liang Sun, and Yubin Gao. "± sign pattern matrices that allow orthogonality." Czechoslovak Mathematical Journal 56, no. 3 (2006): 969–79. http://dx.doi.org/10.1007/s10587-006-0072-y.

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17

Park, Jin-Woo, and Sung-Soo Pyo. "Construction and nonnegativity of sign idempotent sign pattern matrices." Linear Algebra and its Applications 435, no. 11 (2011): 2860–69. http://dx.doi.org/10.1016/j.laa.2011.05.001.

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18

Shao, Jia-Yu, and Hai-Ying Shan. "The determinantal regions of complex sign pattern matrices and ray pattern matrices." Linear Algebra and its Applications 395 (January 2005): 211–28. http://dx.doi.org/10.1016/j.laa.2004.08.023.

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19

Abba, Sani, Usman Sanusi, and Sulaiman Sani. "Permutation Pattern Avoidance in the Alternating Sign Matrices." UMYU Scientifica 3, no. 4 (2024): 386–98. https://doi.org/10.56919/usci.2434.033.

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Study’s Excerpt Aunu permutations (permutations of prime length with their first entry as unity) are explored with a specific focus on involutions. The concept of pattern avoidance is examined using Aunu permutations that avoid the 213 pattern. The results reveal that Catalan numbers count the set of alternating sign matrices. Both bijective and algebraic proofs are provided to support the findings. The study transforms classical ideas, first presented by Abdullahi bin Fodiyo in his book called Da'ulmusalli (light to a worshipper), into modern mathematical science. Full Abstract We represented

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20

Zhang, Ling, Ting-Zhu Huang, and Zhongshan Li. "Primitive Zero-Symmetric Sign Pattern Matrices with Zero Diagonal Attaining the Maximum Base." Journal of Applied Mathematics 2012 (2012): 1–28. http://dx.doi.org/10.1155/2012/276386.

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The base set of primitive zero-symmetric sign pattern matrices with zero diagonal is{1,2,…,2n−1}. In this paper, the primitive zero-symmetric sign pattern matrices with zero diagonal attaining the maximal base2n−1are characterized.

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21

Berliner, Adam H., Derek DeBlieck та Deepak Shah. "Sign pattern matrices that allow inertia 𝕊n". Involve, a Journal of Mathematics 12, № 7 (2019): 1229–40. http://dx.doi.org/10.2140/involve.2019.12.1229.

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22

赵, 心茹. "Some Studies on Toeplitz Sign Pattern Matrices." Advances in Applied Mathematics 12, no. 01 (2023): 332–38. http://dx.doi.org/10.12677/aam.2023.121036.

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23

Jiongsheng, Li, and Gao Yubin. "The structure of tripotent sign pattern matrices." Applied Mathematics-A Journal of Chinese Universities 16, no. 1 (2001): 1–7. http://dx.doi.org/10.1007/s11766-001-0030-2.

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24

Brennan, Zachary, Christopher Cox, Bryan Curtis, et al. "Orthogonal realizations of random sign patterns and other applications of the SIPP." Electronic Journal of Linear Algebra 39 (August 22, 2023): 434–59. http://dx.doi.org/10.13001/ela.2023.7579.

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A sign pattern is an array with entries in $\{+,-,0\}$. A real matrix $Q$ is row orthogonal if $QQ^T = I$. The Strong Inner Product Property (SIPP), introduced in [B.A. Curtis and B.L. Shader, Sign patterns of orthogonal matrices and the strong inner product property, Linear Algebra Appl. 592: 228-259, 2020], is an important tool when determining whether a sign pattern allows row orthogonality because it guarantees there is a nearby matrix with the same property, allowing zero entries to be perturbed to nonzero entries, while preserving the sign of every nonzero entry. This paper uses the SIPP

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25

Pelejo, Diane Christine, and Jean Leonardo Abagat. "On Sign Pattern Matrices that Allow or Require Algebraic Positivity." Electronic Journal of Linear Algebra 35 (February 1, 2019): 331–56. http://dx.doi.org/10.13001/1081-3810.3862.

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A square matrix M with real entries is algebraically positive (AP) if there exists a real polynomial p such that all entries of the matrix p(M) are positive. A square sign pattern matrix S allows algebraic positivity if there is an algebraically positive matrix M whose sign pattern is S. On the other hand, S requires algebraic positivity if matrix M, having sign pattern S, is algebraically positive. Motivated by open problems raised in a work of Kirkland, Qiao, and Zhan (2016) on AP matrices, all nonequivalent irreducible 3 by 3 sign pattern matrices are listed and classify into three groups (

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26

Delgado, Jorge, Héctor Orera, and J. M. Peña. "Accurate Computations with Block Checkerboard Pattern Matrices." Mathematics 12, no. 6 (2024): 853. http://dx.doi.org/10.3390/math12060853.

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In this work, block checkerboard sign pattern matrices are introduced and analyzed. They satisfy the generalized Perron–Frobenius theorem. We study the case related to total positive matrices in order to guarantee bidiagonal decompositions and some linear algebra computations with high relative accuracy. A result on intervals of checkerboard matrices is included. Some numerical examples illustrate the theoretical results.

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27

Delsarte, P., and Y. Kamp. "Low Rank Matrices with a Given Sign Pattern." SIAM Journal on Discrete Mathematics 2, no. 1 (1989): 51–63. http://dx.doi.org/10.1137/0402006.

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28

Hall, Frank J., Zhongshan Li, and Di Wang. "Symmetric sign pattern matrices that require unique inertia." Linear Algebra and its Applications 338, no. 1-3 (2001): 153–69. http://dx.doi.org/10.1016/s0024-3795(01)00381-0.

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29

You, Lihua, and Jian Shen. "A survey on bases of sign pattern matrices." Linear Algebra and its Applications 439, no. 2 (2013): 346–57. http://dx.doi.org/10.1016/j.laa.2013.03.020.

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30

Chen, Wei-Hsu, and Mao-Ting Chien. "Tree sign pattern matrices that require zero eigenvalues." Bulletin of the Australian Mathematical Society 55, no. 1 (1997): 81–88. http://dx.doi.org/10.1017/s0004972700030550.

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31

Mendes Araújo, C., and Juan R. Torregrosa. "Sign pattern matrices that admit M-, N-, P- or inverse M-matrices." Linear Algebra and its Applications 431, no. 5-7 (2009): 724–31. http://dx.doi.org/10.1016/j.laa.2009.03.022.

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32

Bakonyi, Mihaly, Charles R. Johnson, and David P. Stanford. "Sign pattern matrices that require domain-range pairs with given singn patterns." Linear and Multilinear Algebra 44, no. 2 (1998): 165–78. http://dx.doi.org/10.1080/03081089808818556.

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33

Gao, Yubin, and Jiongsheng Li. "On the potential stability of star sign pattern matrices." Linear Algebra and its Applications 327, no. 1-3 (2001): 61–68. http://dx.doi.org/10.1016/s0024-3795(00)00329-3.

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34

Behn, Antonio, Kenneth R. Driessel, Irvin Roy Hentzel, Kent A. Vander Velden, and James Wilson. "Some nilpotent, tridiagonal matrices with a special sign pattern." Linear Algebra and its Applications 436, no. 12 (2012): 4446–50. http://dx.doi.org/10.1016/j.laa.2011.07.001.

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35

Ma, Hongping, and Zhengke Miao. "Imprimitive non-powerful sign pattern matrices with maximum base." Linear and Multilinear Algebra 59, no. 4 (2011): 371–90. http://dx.doi.org/10.1080/03081080903542734.

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36

Wang, Longqin, Lihua You, and Hongping Ma. "Primitive non-powerful sign pattern matrices with base 2." Linear and Multilinear Algebra 59, no. 6 (2011): 693–700. http://dx.doi.org/10.1080/03081087.2010.487067.

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37

Vostrikov, Anton. "Matrix vitrages and regular Hadamard matrices." Information and Control Systems, no. 5 (October 26, 2021): 2–9. http://dx.doi.org/10.31799/1684-8853-2021-5-2-9.

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Introduction: The Kronecker product of Hadamard matrices when a matrix of order n replaces each element in another matrix of order m, inheriting the sign of the replaced element, is a basis for obtaining orthogonal matrices of order nm. The matrix insertion operation when not only signs but also structural elements (ornamental patterns of matrix portraits) are inherited provides a more general result called a "vitrage". Vitrages based on typical quasi-orthogonal Mersenne (M), Seidel (S) or Euler (E) matrices, in addition to inheriting the sign and pattern, inherit the value of elements other t

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38

Bru, Rafael, Maria T. Gassó, Isabel Giménez, and Máximo Santana. "Nonnegative Combined Matrices." Journal of Applied Mathematics 2014 (2014): 1–5. http://dx.doi.org/10.1155/2014/182354.

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The combined matrix of a nonsingular real matrixAis the Hadamard (entrywise) productA∘A-1T. It is well known that row (column) sums of combined matrices are constant and equal to one. Recently, some results on combined matrices of different classes of matrices have been done. In this work, we study some classes of matrices such that their combined matrices are nonnegative and obtain the relation with the sign pattern ofA. In this case the combined matrix is doubly stochastic.

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39

Cheng, Bo, and Bolian Liu. "Primitive zero-symmetric sign pattern matrices with the maximum base." Linear Algebra and its Applications 433, no. 2 (2010): 365–79. http://dx.doi.org/10.1016/j.laa.2010.03.003.

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40

You, Lihua, Jiayu Shao, and Haiying Shan. "Bounds on the bases of irreducible generalized sign pattern matrices." Linear Algebra and its Applications 427, no. 2-3 (2007): 285–300. http://dx.doi.org/10.1016/j.laa.2007.07.019.

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41

Cheng, Bo, and Bolian Liu. "The base sets of primitive zero-symmetric sign pattern matrices." Linear Algebra and its Applications 428, no. 4 (2008): 715–31. http://dx.doi.org/10.1016/j.laa.2007.07.024.

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42

Liang, Yanting, Bolian Liu, and Hong-Jian Lai. "Multi-gbase index of primitive anti-symmetric sign pattern matrices." Linear and Multilinear Algebra 57, no. 6 (2009): 535–46. http://dx.doi.org/10.1080/03081080701861849.

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43

蒋, 思源. "Zero Diagonal Combinatorial Symmetric Sign Pattern Matrices with Order 3." Advances in Applied Mathematics 12, no. 01 (2023): 325–31. http://dx.doi.org/10.12677/aam.2023.121035.

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44

焦, 旸. "4-Order Hessenberg Sign Pattern Matrices That Allow Algebraic Positivity." Advances in Applied Mathematics 12, no. 02 (2023): 582–89. http://dx.doi.org/10.12677/aam.2023.122061.

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45

Curtis, Bryan, Colin Garnett, Bryan L. Shader, and Kevin N. Vander Meulen. "The non-symmetric strong multiplicity property for sign patterns." Electronic Journal of Linear Algebra 41 (February 20, 2025): 153–65. https://doi.org/10.13001/ela.2025.8827.

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We develop a non-symmetric strong multiplicity property for matrices that may or may not be symmetric. We say a sign pattern allows the non-symmetric strong multiplicity property if there is a matrix with the non-symmetric strong multiplicity property that has the given sign pattern. We show that this property of a matrix pattern preserves multiplicities of eigenvalues for superpatterns of the pattern. We also provide a bifurcation lemma, showing that a matrix pattern with the property also allows refinements of the multiplicity list of eigenvalues. We conclude by demonstrating how this proper

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46

Sun, Lizhu, Wenzhe Wang, Changjiang Bu, Yimin Wei, and Baodong Zheng. "Representations and sign pattern of the group inverse for some block matrices." Electronic Journal of Linear Algebra 30 (February 8, 2015): 744–59. http://dx.doi.org/10.13001/1081-3810.3169.

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Let $M= \left[ \begin{array}{cc} A& B \\ C& O \end{array} \right]$ be a complex square matrix where A is square. When BCB^{\Omega} =0, rank(BC) = rank(B) and the group inverse of $\left[ \begin{array}{cc} B^{\Omega} A B^{\Omega} & 0 \\ CB^{\Omega} & 0 \right]$ exists, the group inverse of M exists if and only if rank(BC + A)B^{\Omega}AB^{\Omega})^{\pi}B^{\Omega}A)= rank(B). In this case, a representation of $M^#$ in terms of the group inverse and Moore-Penrose inverse of its subblocks is given. Let A be a real matrix. The sign pattern of A is a (0,+,â)-matrix obtained from A

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47

Liu, Bolian, and Lihua You. "Bounds on the base of primitive nearly reducible sign pattern matrices." Linear Algebra and its Applications 418, no. 2-3 (2006): 863–81. http://dx.doi.org/10.1016/j.laa.2006.03.024.

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48

Catral, M., D. D. Olesky, and P. van den Driessche. "Allow problems concerning spectral properties of sign pattern matrices: A survey." Linear Algebra and its Applications 430, no. 11-12 (2009): 3080–94. http://dx.doi.org/10.1016/j.laa.2009.01.031.

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49

Fang, Wei, Wei Gao, Yubin Gao, et al. "Rational realization of the minimum ranks of nonnegative sign pattern matrices." Czechoslovak Mathematical Journal 66, no. 3 (2016): 895–911. http://dx.doi.org/10.1007/s10587-016-0299-1.

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50

Shao, Jia-Yu, Yue Liu, and Ling-Zhi Ren. "The inverse problems of the determinantal regions of ray pattern and complex sign pattern matrices." Linear Algebra and its Applications 416, no. 2-3 (2006): 835–43. http://dx.doi.org/10.1016/j.laa.2005.12.025.

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