2 2 2 1 ] . Compute the eigenvalues and eigenspaces of A. We

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.
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Eigenspaces of a Matrix Calculator

(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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Eigenvalues and Eigenvectors Calculator

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
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Find bases for eigenspaces of A

forms 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