Eigenvalues and Eigenvectors - Eigenvectors and Eigenvalues
3 important questions on Eigenvalues and Eigenvectors - Eigenvectors and Eigenvalues
An eigenvector of an n x n matrix A is a nonzero vector x such that A*x = lambda*x for some scalar lambda. When is the scalar lambda called an eigenvalue of A?
If there is a nontrivial solution x of A*x = lambda*x; such an x is called an eigenvector corresponding to lambda.
Theorem 1
The eigenvalues of a triangular matrix are?
The entries on its main diagonal.
Theorem 2
If v1, ..., vr are eigenvectors that correspond to distinct eigenvalues lambda1, ... lambdar of an n x n matrix A, then what can be said about the set {v1, ..., vr}
The set is linearly independent.
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