 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-2-of-the-natural-sciences-course-of-the-university-of-cambridge/2018/paper-1/6/a/solution

A

P

makes

P^{- 1} A P

A

For example,

(1002) is diagonalizable, (1011) is not diagonalizable .

The first is already diagonal. The second has only the eigenvalue one, of algebraic multiplicity two, but its eigenspace consists of

(x, 0)^{T}

and has dimension one. It cannot supply a two-vector eigenbasis.

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