The Jordan canonical form exists if this function splits completely over the base field.
This function can be defined as the product of elementary divisors of its associated map. The Jordan canonical form exists if this function splits completely over the base field. This function annihilates its associated map, by the (*) Cayley-Hamilton theorem. This function's zeroes lie on the unit circle for a unitary map. If the geometric multiplicity is less than the algebraic multiplicity of one of this function's zeroes, then the associated map is not diagonalizable. This function's constant term is the determinant. This function can be computed by taking the determinant of its associated map minus λI. For 10 points, name this polynomial whose roots are the eigenvalues of its associated linear map.
This function can be defined as the product of elementary divisors of its associated map.
characteristic polynomial [or characteristic equation]