Quick way to find Eigenvalues

Method

Eigenvalues

$${\lambda }_{1,2}=m\pm \sqrt{m^2-p}$$

Where

• $m\to$ Mean of the Eigen Values (diagonal)
• $p\to$ product of the Eigen Values (determinant)

IMPORTANT: Order eigenvalues from largest to smallest

$${\lambda }_1\ge {\lambda }_2$$

Example

$$\left[\begin{array}{ll}3& 1\\ 4& 1\end{array}\right]$$

Eigenvalues

• Mean

  $$m=\frac{3+1}{2}=2$$

• Product

  $$p=3-4=-1$$

IMPORTANT: Order eigenvalues from largest to smallest:

$$\boxed{\Rightarrow {\lambda }_1,{\lambda }_2=2\pm \sqrt{5}}$$