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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