monic polynomial การใช้

• Any monic polynomial is the characteristic polynomial of its companion matrix.
• Notably, the product of monic polynomials again is monic.
• It is the monic polynomial of least degree in.
• This is stronger than the statement that any integral element satisfies some monic polynomial.
• The cyclotomic polynomials are monic polynomials with integer coefficients that are palindromics of even degree.
• This implies that, over, there are exactly } } irreducible monic polynomials of degree.
• In the case of rational functions the denominator could similarly be required to be a monic polynomial.
• In mathematics, it is common to require that the greatest common divisor be a monic polynomial.
• The "'minimal polynomial "'is thus defined to be the monic polynomial which generates.
• To exclude such examples, sometimes it is defined that PI-rings must satisfy a monic polynomial identity.
• As does not have any multiple factor, it is thus the product of all the irreducible monic polynomials that divide it.
• "Monic multivariate polynomials " according to either definition share some properties with the " ordinary " ( univariate ) monic polynomials.
• There is a unique monic polynomial of minimal degree which annihilates " A "; this polynomial is the minimal polynomial.
• It is assumed that " I " contains monic polynomials when PI-rings are required to satisfy monic polynomial identities.
• It is assumed that " I " contains monic polynomials when PI-rings are required to satisfy monic polynomial identities.
• The Bernstein Sato polynomial is the monic polynomial of smallest degree amongst such " b " ( " s " ).
• The degree of this identity is optimal since the matrix ring can not satisfy any monic polynomial of degree less than 2 " m ".
• In linear algebra, the "'minimal polynomial "'of an field is the monic polynomial over of least degree such that 0 } }.
• I have to prove that the greatest common divisor, d ( x ) ( which is defined as a monic polynomial ) is an associate of h ( x ).
• For every " n "-tuple of complex numbers, there is exactly one monic polynomial of degree " n " that has them as its zeros ( keeping multiplicities ).