As a corollary of this, one finds that the degree of the minimal polynomial for a constructible point ( and therefore of any constructible length ) is a power of 2.
42.
Therefore, just having for both matrices some decomposition of the space into cyclic subspaces, and knowing the corresponding minimal polynomials, is not in itself sufficient to decide their similarity.
43.
What if I just wanted the degree of the minimal polynomial and didn't care about the actual coefficients ? talk ) 01 : 10, 10 January 2017 ( UTC)
44.
If a projection is nontrivial it has minimal polynomial x ^ 2-x = x ( x-1 ), which factors into distinct roots, and thus P is diagonalizable.
45.
However, the periodic representation does not derive from an algorithm defined over all real numbers and it is derived only starting from the knowledge of the minimal polynomial of the cubic irrational.
46.
Like the characteristic polynomial, the minimal polynomial does not depend on the base field, in other words considering the matrix as one with coefficients in a larger field does not change the minimal polynomial.
47.
Like the characteristic polynomial, the minimal polynomial does not depend on the base field, in other words considering the matrix as one with coefficients in a larger field does not change the minimal polynomial.
48.
Then 3 + sqrt ( 2 ) is a unit in this ring, because its minimal polynomial is x 2-6x + 1 ( its associate is 3-sqrt ( 2 ) ).
49.
:: : : See Minimal polynomial ( field theory ) ?" Alternative proof of uniqueness " ( can't seem to get a working link to that sub-section ).
50.
By extension, the "'Mahler measure of an algebraic number "'\ alpha is defined as the Mahler measure of the minimal polynomial of \ alpha over \ mathbb { Q }.
