Eigenvalues and Eigenvectors

From Department of Mathematics at UTSA
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Definition

In linear algebra, an eigenvector of a matrix is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denoted by , is the factor by which the eigenvector is scaled. That is, given some eigenvector of a square matrix , , where is the corresponding eigenvalue of . For example:

Let ,


Thus, is an eigenvector of matrix , and its corresponding eigenvalue .

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