Question
Find eigenvalues of matrix:
$$ A = \left[ \begin{matrix}0&\dfrac{ 1 }{ 2 }\\\dfrac{ 1 }{ 2 }&0\end{matrix} \right] $$Answer
The eigenvalues of matrix A are:
$$ \lambda_1 = \dfrac{ 1 }{ 2 } ~ \text{ and } ~ \lambda_2 = -\dfrac{ 1 }{ 2 } $$Explanation
Step 1 : The characteristic polynomial for matrix A is:
$$ p(\lambda) = \lambda^2-\frac{ 1 }{ 4 } $$
Step 2 : Eigenvalues are roots of the characteristic polynomial, so the equation
$$ \lambda^2-\frac{ 1 }{ 4 } = 0 $$yields the above eigenvalues.
( click here to view an explanation on how to solve this equation.)
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