Eigenvalues and eigenvectors defined

For this to hold true for ip 0, the matrix (A — XI) must be singular, providing a characteristic polynomial of degree N, 

Before discussing general eigenvector properties, let us consider the case of a 2x 2 real matrix, for which analytical calculation of eigenvalues is easy, 

we have the following properties for a real 2x 2 matrix  

note that the determinant equals the product of the eigenvalues, 

We now consider some special cases of 2 x 2 real matrices. 

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