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First step: find the eigenvalues, via the characteristic polynomial det ( A − λ I) = | 6 − λ 4 − 3 − 1 − λ | = 0 λ 2 − 5 λ + 6 = 0. One of the eigenvalues is λ 1 = 2. You find the other one.

(Definition) For a matrix M M having for eigenvalues λi λ i, an eigenspace E E associated with an eigenvalue λi λ i is the set (the basis) of eigenvectors →vi v i → which have the same

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So the eigenspace is simply the null space of the matrix ???\lambda I_n-A???.???E_\lambda=N(\lambda I_n-A)??? To find the matrix ???\lambda I_n-A???, we can

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So that's a new word, eigenspace. Eigenspace just means all of the eigenvectors that correspond to some eigenvalue. The eigenspace for some particular eigenvalue is going to be equal to the set of vectors

Get Startedforms a vector space called the eigenspace of A correspondign to the eigenvalue λ. Since it depends on both A and the selection of one of its eigenvalues, the notation will be used to