minimal polynomial sentence in Hindi
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- Where the minimal polynomial is identical to the characteristic polynomial, the Frobenius normal form is the companion matrix of the characteristic polynomial.
- There is a unique monic polynomial of minimal degree which annihilates " A "; this polynomial is the minimal polynomial.
- Any polynomial which annihilates " A " ( such as the characteristic polynomial ) is a multiple of the minimal polynomial.
- *PM : examples of minimal polynomials, id = 9184 new !-- WP guess : examples of minimal polynomials-- Status:
- *PM : examples of minimal polynomials, id = 9184 new !-- WP guess : examples of minimal polynomials-- Status:
- *PM : existence of the minimal polynomial, id = 4723-- WP guess : existence of the minimal polynomial-- Status:
- *PM : existence of the minimal polynomial, id = 4723-- WP guess : existence of the minimal polynomial-- Status:
- If \ varphi is not injective, let " p " ( X ) be a generator of its minimal polynomial of ?.
- This statement is equivalent to saying that the minimal polynomial of " A " divides the characteristic polynomial of " A ".
- Similarly ( 6, 15, 40 ) gives a matrix of which also has rank 3 when the degree of the minimal polynomial is 4.
- Now, is easily seen to be Gauss's Lemma, is also irreducible over, and is thus a minimal polynomial over for } }.
- Let K ( \ alpha ) be an algebraic field extension generated by an element \ alpha, which has P ( x ) as minimal polynomial.
- If is a matrix with positive eigenvalues and minimal polynomial, then the Jordan decomposition into generalized eigenspaces of can be deduced from the partial fraction expansion of.
- This implies in particular that an integral element over an integrally closed domain " A " has a minimal polynomial over " A ".
- In linear algebra, the "'minimal polynomial "'of an field is the monic polynomial over of least degree such that 0 } }.
- The minimal polynomial always divides the characteristic polynomial, which is one way of formulating the Cayley Hamilton theorem ( for the case of matrices over a field ).
- A " separable extension " is an extension that may be generated by " separable elements ", that is elements whose minimal polynomials are separable.
- By taking appropriate sums of conjugates of, following the construction of Gaussian periods, one can find an element of that generates over, and compute its minimal polynomial.
- By finding the minimal polynomial of x in this ring, we have computed p _ i ( x ), and thus factored p ( x ) over K.
- The minimal polynomial of " x " divides every polynomial which has " x " as a root ( this is Abel's irreducibility theorem ).
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