Learn Linear Algebra

Theorem

The eigenvalues of a triangular matrix are the entries on its main diagonal.

Theorem

If v1,,vr \vec{v}_1, \dots, \vec{v}_r are eigenvectors that correspond to distinct eigenvalues λ1,,λr \lambda_1, \dots, \lambda_r of an n×n n \times n matrix A A , then the set {v1,,vr} \{ \vec{v}_1, \dots, \vec{v}_r \} is linearly independent.