# Why do the eigenvalues of a triangular matrix lie on its diagonal?

Suppose is a triangular matrix, so is invertible. Now with eigenvalues finding process, we can only shift each ‘s diagonal entry for a to make non-invertible. And the only possible way is to shift each ‘s diagonal entry for a ** that is also an ‘s diagonal entry**, so after that one diagonal entry of will equal to zero and is then non-invertible.

Hence the eigenvalues of a triangular matrix lie on its diagonal.