Exercise 12

Translation endomorphism on polynomials

Theory used: Eigenvalues of an endomorphism via the associated matrix Algebraic and geometric multiplicity Diagonalizability criterion

Let $f : R_{2} [x] \to R_{2} [x]$ be the endomorphism defined by $f (p (x)) = p (x + 1)$ . Determine the eigenvalues and eigenspaces of $f$ and determine whether $f$ is diagonalizable.

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