# complex eigen values of a linear map

$a$ in that case $T$ is not invertible hence $T$ is not injective and surjective. hence $(a)$ is true statement. am I right?

$b$ need not be.

$c$ is true as a three dimensional eigen space is invariant hence if I restrict characteristic polynomial on that space it is three degree must have a real root.is my intuition right? please help.

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All sound good. – user1551 Dec 18 '12 at 8:10

$$T=\begin{pmatrix}2&0&0&...&0\\0&2&0&...&0\\..&..&..&..&..\\0&0&...&0&2\end{pmatrix}$$