Eigenvalues, Eigenvectors, and Diagonalization
Find all of the eigenvalues and eigenvectors of A= 1 1 0 1 : The characteristic polynomial is ( 1)2, so we have a single eigenvalue = 1 with algebraic multiplicity 2. The matrix A I= 0 1 0 0 has a one-dimensional null space spanned by the vector (1;0). Thus, the geometric multiplicity of this eigenvalue is 1.
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