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Null Values and Null Vectors of Matrix Pencils and their Applications in Linear System Theory

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2017, Master of Science in Engineering (MSEgr), Wright State University, Electrical Engineering.
Considerable literature exists in linear algebra to solve the generalized eigenvalue, eigenvector problem (F - λ G)v = 0 where F, G ∈ ℜ(s × s), are square matrices. However, a number of applications lend themselves to the case where F, G ∈ ℜ(s × t), and st. The existing methods cannot be used for such non-square cases. This research explores structural decomposition of a matrix pencil (F - λ G), s ≠ t to compute finite values of λ for which rank(F - λ G) < min(s,t). Moreover, from the decomposition of the matrix pencil, information about the order of λ at infinity, the Kronecker row and column indices of a matrix pencil can also be extracted. Equally important is the computation of non-zero vectors w ∈ ℜ(1 × s) and v ∈ ℜ(t × 1) corresponding to each finite value of λ, such that w(F - λ G) = 0 and (F - λ G)v = 0. Algorithms are developed for the computation of λ, w, and v using numerically efficient techniques. Proposed algorithms are applied to problems encountered in system theory and illustrated by means of numerical examples.
Pradeep Misra, Ph.D. (Advisor)
Xiaodong Zhang, Ph.D. (Committee Member)
Luther Palmer III, Ph.D. (Committee Member)
58 p.

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Citations

  • Dalwadi, N. (2017). Null Values and Null Vectors of Matrix Pencils and their Applications in Linear System Theory [Master's thesis, Wright State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=wright1511633137571704

    APA Style (7th edition)

  • Dalwadi, Neel. Null Values and Null Vectors of Matrix Pencils and their Applications in Linear System Theory. 2017. Wright State University, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=wright1511633137571704.

    MLA Style (8th edition)

  • Dalwadi, Neel. "Null Values and Null Vectors of Matrix Pencils and their Applications in Linear System Theory." Master's thesis, Wright State University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=wright1511633137571704

    Chicago Manual of Style (17th edition)