16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 7.3.5

The Rational and Jordan Forms

Mathematics — Linear Algebra · jordan-form-differentiation-operator

Problem

The differentiation operator on the space of polynomials of degree less than or equal to

3

is represented in the `natural' ordered basis by the matrix

\begin{bmatrix} 0 & 1 & 0 & 0 \\ 0 & 0 & 2 & 0 \\ 0 & 0 & 0 & 3 \\ 0 & 0 & 0 & 0 \end{bmatrix}.

What is the Jordan form of this matrix? (

F

a subfield of the complex numbers.)