Thread: show any square matrix in C has at least one eigenvalue

show any square matrix in C has at least one eigenvalue

Originally Posted by silversand

show any square matrix in C has at least one eigenvalue

An 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.