Answer by Fred for Is this eigenvalue property true?
If $p$ is a polynomial and we denote the set of eigenvalues of $A$ by $E_A$ then the spectral mapping property is valid:$E_{p(A)}=p(E_A)$.In your situation: $p(x)=x- \mu$
View ArticleAnswer by Johan Löfberg for Is this eigenvalue property true?
Yes, by definition you have $Ax = \lambda x$ for the eigenvalue/eigenvector pairs, and thus $(A - \mu I)x = Ax - \mu x = \lambda x - \mu x = (\lambda - \mu)x$.
View ArticleIs this eigenvalue property true?
Does the following property hold for any matrix $A_n \in \mathbb R^{n x n}$?The set of eigenvalues of $A_n - \mu I_n$ is $\{ \lambda_i(A)-\mu \}_{i=1}^n$.
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