Suppose I have a p-component non-null column vector $\mathbf{a}$. Then what will be the eigen roots of the matrix $\mathbf{A} = \mathbf{aa'}$.
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$\begingroup$ Welcome to MathSE. When you pose a question here, you are expected to share your own thoughts on the problem. Please edit your question to show any work you have done on the problem and to indicate where you are stuck so that you receive responses that address the specific difficulties you are encountering. $\endgroup$– N. F. TaussigJul 13, 2015 at 9:41
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$\begingroup$ what do you mean by eigen roots? $\endgroup$– user251257Jul 13, 2015 at 10:07
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1 Answer
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Since, $A = a a' $ We get,
$$A^2 = (a'a) A$$ Using this we can get the characteristic equation as:
$$ \lambda^p = (a'a) \lambda^{p-1}$$
Now solve the equation and you will get your answer.
