 Solution

ID: past-exam-of-the-algebra-analysis-and-differential-equations-1-course-of-the-university-of-oxford/2010/1/b/solution

In the adapted basis from part (a), the matrix has

r

diagonal entries equal to one and

N - r

equal to zero. With the characteristic polynomial convention

χ_{E} (X) = det (X I - E)

χ_{E} (X) = X^{N - r} (X - 1)^{r} .

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