**Characteristic Polynomial**,

**Eigenspace**

The solution space of is called the *eigenspace* of associated with the eigenvalue . The eigenspace is denoted by .

**Sum/Product of Eigenvalues**

– The sum of all eigenvalues of (including repeated eigenvalues) is the same as (trace of , i.e. the sum of diagonal elements of )

– The product of all eigenvalues of (including repeated eigenvalues) is the same as .