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.