Publication Date


Document Type


Committee Members

Pradeep Misra (Advisor), Luther Palmer III (Committee Member), Xiaodong Zhang (Committee Member)

Degree Name

Master of Science in Engineering (MSEgr)


Considerable literature exists in linear algebra to solve the generalized eigenvalue, eigenvector problem (F − [lambda]G)v = 0 where F, G 2 Rs×s, are square matrices. However, a number of applications lend themselves to the case whereF, G 2 Rs×, and s ≠ t. The existing methods cannot be used for such non-square cases. This research explores structural decomposition of a matrix pencil (F − [lambda]G), s 6≠ t to compute finite values of [lambda] for which rank (F − [lambda]G) < min(s, t). Moreover, from the decomposition of the matrix pencil, information about the order of [lambda] 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 2 R1×s and v 2 Rt×1 corresponding to each finite value of [lambda], such that w(F - [lambda] G) = 0 and (F - [lambda]G)v = 0. Algorithms are developed for the computation of lambda, w, and v using numerically efficient techniques. Proposed algorithms are applied to problems encountered in system theory and illustrated by means of numerical examples.

Page Count


Department or Program

Department of Electrical Engineering

Year Degree Awarded