## ABSTRACT

The study of many problems in engineering and science gives rise to what is known as the algebraic eigenvalue problem. The problem involves finding for

what values of the parameter l the system of linear algebraic equations

a11x1a12x2a13x3 . . .a1nxnl x1 a21x1a22x2a23x3 . . .a2nxnl x2

an1x1an2x2an3x3 . . .annxnl xn,

has non-trivial solutions (not all the x1, x2, . . . , xn vanish), and then finding

the form of these solutions.