# Math Help - show any square matrix in C has at least one eigenvalue

1. ## show any square matrix in C has at least one eigenvalue

show any square matrix in C has at least one eigenvalue

2. Originally Posted by silversand
show any square matrix in C has at least one eigenvalue
An $n \times n$ matrix will always yield a characteristic equation which is a polynomial of order n.

By the fundamental theorem of algebra, any non-constant single variable polynomial with complex coefficients has at least 1 complex root. Eigenvalues are roots of the characteristic equation.