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    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 Preview

    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 ...

    Solution Summary

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