When we have LINEARLY INDEPENDENT EIGENVECTORS (detailed proof) // Short Lecture // Linear Algebra

We prove that when we have distinct eigenvalues we get linearly independent eigenvectors. This allows us to know when the eigenvectors of an nxn matrix form a basis for R^n. 0:00 example of eigenvectors forming a basis for R^2 2:08 statement of theorem: distinct eigenvalues correspond to linearly independent eigenvectors 3:09 detailed proof 11:27 takeaway Application: Diagonalization of matrices    • DIAGONALIZE matrices // Short Lecture // L...