Question
Find eigenvalues of matrix:
$$ A = \left[ \begin{matrix}\dfrac{ 5 }{ 3 }&0\\0&\dfrac{ 1 }{ 3 }\end{matrix} \right] $$Answer
The eigenvalues of matrix A are:
$$ \lambda_1 = \dfrac{ 1 }{ 3 } ~ \text{ and } ~ \lambda_2 = \dfrac{ 5 }{ 3 } $$Explanation
Step 1 : The characteristic polynomial for matrix A is:
$$ p(\lambda) = \lambda^2-2\lambda+\frac{ 5 }{ 9 } $$
Step 2 : Eigenvalues are roots of the characteristic polynomial, so the equation
$$ \lambda^2-2\lambda+\frac{ 5 }{ 9 } = 0 $$yields the above eigenvalues.
( click here to view an explanation on how to solve this equation.)
This page was created using
Eigenvalues calculator