Problems of the form
where, typically, an overconstrained system of equations is given (say
equations in n unknowns), where each
also depends on
an additional parameter
are called eigenvalue
problems. This system has a solution
only for specific values of
. Each
is an
eigenvalue of the system, and the corresponding solution
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 . We can formulate
this problem as follows: Given a real or complex
matrix
, find all
such that the system of
equations
¯has a solution¯
¯ = 0
= 1