MATH 2210Q Chapter Notes - Chapter 5: Diagonalizable Matrix, Royal Institute Of Technology, Lek Mating
18 Dec 2017
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Eigenvector - of an n n scalar matrix a is a nonzero vector x such that x x. Eigenvalue (scalar ) of a - if there is a nontrivial solution x of. X is an eigenvector corresponding to . Check if a vector is an eigenvector of a x. Is an eigenvalue if (a- i) x =0 has a nontrivial solution. There can be many (linearly dependent) eigenvectors from an eigenvalue. N set is a subspace of (consists of the zero vector) Eigenspace - set of all solutions of (a- i) x =0 is the null space of the matrix a- i and the. Thm 1: the eigenvalues of a triangular matrix are the entries on its main diagonal. *note: 0 is an eigenvalue of a if and only if a is not invertible. Thm 2: if n n are eigenvectors that correspond to distinct eigenvalues v1 matrix a , then the set {
