Linear Algebra Chapter 5 & 6 Theorems and Definitions

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5 Terms

1
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Eigenvector of an nxn matrix A

A non-zero vector x suh that Ax = λ for some scalar λ

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Eigenvalue

Some scalar λ of A if there is a non-trivial solution x of Ax = λx; such an x is called an eigenvector corresponding to λ

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What are the eigenvalues of a triangular matrix?

The entries on the main diagonal of the matrix

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What does it mean if the eigenvectors {v1 … vr} correspond to distinct eigen values λ1 … λr of an nxn matrix?

The set {v1 … vr} is linearly dependent

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A scalar λ is an eigenvalue of an nxn matrix A if and only if λ satisfies what?

The characteristic equation