Let $A$ be complex $2×2$ matrices s.t. $A^2=0$. Which of the following statements are true?
- $PAP^{-1}$ is diagonal for some $2×2$ real matrix $P$.
- $A$ has $2$ distinct eigenvalues in $\Bbb C$.
- $A$ has $1$ eigenvalue in $\Bbb C$ with multiplicity $2$.
- $Av=v$ for $v\in \Bbb C^2 ,v≠0$.
Eigenvalues of complex $2×2$ matrices
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linear-algebra
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0not getting any A s.t. A^2=0. – 2012-12-17
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0where to begin ....please suggest me........... – 2012-12-17
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0Take $A=\begin{pmatrix}a&a\\-a&-a\end{pmatrix}$ for any $a\in\mathbb{C}$, for exmaple. – 2012-12-17
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02 is wrong ........ 3 is correct.......... – 2012-12-17
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0That's right. Can you prove it? – 2012-12-17
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0what about 1 and 4.............. – 2012-12-17
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0Check that $(PAP^{-1})^2=PA^2P^{-1}$. What can you conclude about 1? – 2012-12-17
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0I can't find 4 but1 is looking right – 2012-12-17
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0where to begin ....please suggest me for 4... – 2012-12-17