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Introduction

Problems of the form

displaymath279

where, typically, an overconstrained system of equations is given (say equations in n unknowns), where each tex2html_wrap_inline285 also depends on an additional parameter tex2html_wrap_inline287 are called eigenvalue problems. This system has a solution tex2html_wrap_inline289 only for specific values of tex2html_wrap_inline287 . Each tex2html_wrap_inline293 is an eigenvalue of the system, and the corresponding solution tex2html_wrap_inline295 is the eigensolution.

We shall deal with a specific form of this problem, where all but one of the equations are linear in x and tex2html_wrap_inline287 . We can formulate this problem as follows: Given a real or complex tex2html_wrap_inline301 matrix tex2html_wrap_inline303 , find all tex2html_wrap_inline305 such that the system of equations

 ¯  tex2html_wrap_inline309  ¯  tex2html_wrap_inline311  ¯ = 0

tex2html_wrap_inline313 = 1

has a solution tex2html_wrap_inline315 .



Dinesh Manocha
Mon Apr 20 01:33:57 EDT 1998