Characteristic polynomial of $$$\left[\begin{array}{c}i a g h m n r s t^{2} e^{e i n o r s^{2}}\end{array}\right]$$$

Find the characteristic polynomial of $$$\left[\begin{array}{c}i a g h m n r s t^{2} e^{e i n o r s^{2}}\end{array}\right]$$$.

Start from forming a new matrix by subtracting $$$\lambda$$$ from the diagonal entries of the given matrix:

$$$\left[\begin{array}{c}i a g h m n r s t^{2} e^{e i n o r s^{2}} - \lambda\end{array}\right]$$$

The characteristic polynomial is the determinant of the obtained matrix:

$$$\left|\begin{array}{c}i a g h m n r s t^{2} e^{e i n o r s^{2}} - \lambda\end{array}\right| = i a g h m n r s t^{2} e^{e i n o r s^{2}} - \lambda$$$ (for steps, see determinant calculator).

The characteristic polynomial is $$$p{\left(\lambda \right)} = i a g h m n r s t^{2} e^{e i n o r s^{2}} - \lambda$$$A.