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Linear and Multilinear Algebra Volume 59, 2011 - Issue 6
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Original Articles

Extremal ranks of a quadratic matrix expression with applications

Yongge Tian China Economics and Management Academy, Central University of Finance and Economics, Beijing 100081, ChinaCorrespondence[email protected]
Pages 627-644 | Received 09 Apr 2009, Accepted 13 Mar 2010, Published online: 31 Mar 2011

Citations (12)

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Read on this site (2)

Yongge Tian. (2018) How to establish exact formulas for calculating the max–min ranks of products of two matrices and their generalized inverses. Linear and Multilinear Algebra 66:1, pages 22-73.
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Zhiping Xiong & Yingying Qin. (2015) An invariance property related to the mixed-type reverse order laws. Linear and Multilinear Algebra 63:8, pages 1621-1634.
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Articles from other publishers (10)

Lifang DAI, Maolin LIANG & Yonghong SHEN. (2021) Some Rank Formulas for the Yang-Baxter Matrix Equation AXA = XAX . Wuhan University Journal of Natural Sciences 26:6, pages 459-463.
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Yongge Tian. (2020) A family of 512 reverse order laws for generalized inverses of a matrix product: A review. Heliyon 6:9, pages e04924.
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Bo Jiang & Yongge Tian. (2018) Necessary and sufficient conditions for nonlinear matrix identities to always hold. Aequationes mathematicae 93:3, pages 587-600.
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Yongge Tian & Bo Jiang. (2018) Closed-form formulas for calculating the max–min ranks of a triple matrix product composed by generalized inverses. Computational and Applied Mathematics 37:5, pages 5876-5919.
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Yongge Tian. (2016) Equalities and inequalities for ranks of products of generalized inverses of two matrices and their applications. Journal of Inequalities and Applications 2016:1.
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Zhiping Xiong. (2014) Inequalities for ranks of matrix expressions involving generalized inverses. Journal of Inequalities and Applications 2014:1.
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Yongge Tian. (2012) Equalities and inequalities for Hermitian solutions and Hermitian definite solutions of the two matrix equations AX = B and AXA * = B. Aequationes mathematicae 86:1-2, pages 107-135.
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Yongge Tian. (2012) Formulas for calculating the extremum ranks and inertias of a four-term quadratic matrix-valued function and their applications. Linear Algebra and its Applications 437:3, pages 835-859.
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Yongge Tian. (2012) Solving optimization problems on ranks and inertias of some constrained nonlinear matrix functions via an algebraic linearization method. Nonlinear Analysis: Theory, Methods & Applications 75:2, pages 717-734.
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Yonghui Liu & Yongge Tian. (2010) Max-Min Problems on the Ranks and Inertias of the Matrix Expressions A−BXC±(BXC)∗ with Applications. Journal of Optimization Theory and Applications 148:3, pages 593-622.
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