# Linear Algebra: Eigenvalues

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Find eigenvalues and eigenvectors of the matrix

A=(2 1

9 2)

By transforming the matrix in the basis of eigenvectors, show explictly that the matrix can diagonalized in the eigenvector basis.

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##### Solution Summary

Eigenvalues of a matrix are found. Diagonalization is shown. Transforming a matrix in the basis of eigenvectors are determined.

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The definition of an eigenvalue is:

AX = LX where L is the eigenvalue (lambda)

Which can be rewritten:

(LI-A)X = 0, where I is the identity matrix.

So, that brings us to the characteristic polynomial in our 5 line review:

c(x) = det(xI - A)

The eigenvalues are the roots of this ...

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