Kunze Linear Algebra · Problem 7.3.5

Rational and Jordan Forms

Mathematics — Methods · jordan-form-differentiation

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 [0100002000030000].\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? (FF a subfield of the complex numbers.)

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