What is it?
In Linear Algebra, eigenvalues are scalars associated with square matrices, such that exists a non-zero vector, called the eigenvector, which satisfies the following equation:
In this case, when a matrix is multiplied by a eigenvector , the result is a scaled version of , scaled by the eigenvalue .
How to discover eigenvalues
To discover eigenvalues of a square matrix, one would need to isolate from the past formula, resulting in:
Where is a identity matrix, of the same dimensions as . This happens because identity matrices have the same property as in Matrix Multiplication.
Now, we can solve for . When calculating the determinant of the matrix, we will get its characteristic polynomial, which its roots would be the eigenvalues itself.
Now, with the characteristic polynomial on hands, we just need to find its roots.