Part CCSIR NET December 2023reading-jordan-blocks

Reading jordan blocks

Suppose a 7 × 7 block diagonal complex matrix A has blocks (0), (1), [[0, 1], [0, 0]] and the 3×3 block with $2 π i$ on the diagonal, a 1 in position (1,2) and zeros elsewhere, along the diagonal. Which of the following statements are true?

A.The characteristic polynomial of A is $x^{3} (x - 1) (x - 2 π i)^{3}$ .
B.The minimal polynomial of A is $x^{2} (x - 1) (x - 2 π i)^{3}$ .
C.The dimensions of the eigenspaces for $0, 1, 2 π i$ are 2, 1, 3 respectively.
D.The dimensions of the eigenspaces for $0, 1, 2 π i$ are 2, 1, 2 respectively.

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Reading jordan blocks

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