Information om | Engelska ordet FROBENIUS

Exempel på hur man kan använda FROBENIUS i en mening

• The norm derived from this inner product is called the Frobenius norm, and it satisfies a submultiplicative property, as can be proven with the Cauchy–Schwarz inequality:.
• In 1912 he started studies in mathematical physics at the University of Budapest, with summer visits to the University of Berlin and the University of Göttingen, where he attended lectures by Frobenius and Hilbert, amongst others.
• It was discovered by Augustin Louis Cauchy and Ferdinand Georg Frobenius, and became well-known after William Burnside quoted it.
• ; Frobenius field: A pseudo algebraically closed field whose absolute Galois group has the embedding property.
• The theorem is a collection of results generalizing the significant facts about the decomposition of the regular representation of any finite group, as discovered by Ferdinand Georg Frobenius and Issai Schur.
• Ferdinand Georg Frobenius was born on 26 October 1849 in Charlottenburg, a suburb of Berlin, from parents Christian Ferdinand Frobenius, a Protestant parson, and Christine Elizabeth Friedrich.
• Deligne's contribution was to supply the estimate of the eigenvalues of the Frobenius endomorphism, considered the geometric analogue of the Riemann hypothesis.
• One can also express the condition for a foliation to be defined as a reduction of the tangent bundle to a block matrix subgroup - but here the reduction is only a necessary condition, there being an integrability condition so that the Frobenius theorem applies.
• that it be tangent to a codimension one foliation on the manifold, whose equivalence is the content of the Frobenius theorem.
• More generally, a ring of characteristic p (p a prime) is called perfect if the Frobenius endomorphism is an automorphism.
• When the field of definition is a finite field, there are always non-trivial endomorphisms of an elliptic curve, coming from the Frobenius map, so every such curve has complex multiplication (and the terminology is not often applied).
• There are generalisations, involving the distribution of Frobenius elements in Galois groups involved in the Galois representations on étale cohomology.
• The theorem generalizes the existence theorem for ordinary differential equations, which guarantees that a single vector field always gives rise to integral curves; Frobenius gives compatibility conditions under which the integral curves of r vector fields mesh into coordinate grids on r-dimensional integral manifolds.
• In 1901, he graduated summa cum laude under Frobenius and Lazarus Immanuel Fuchs with his dissertation On a class of matrices that can be assigned to a given matrix, which contains a general theory of the representation of linear groups.
• This gives a local foliation of the subspace because it satisfies integrability conditions (Frobenius theorem).
• In 1925, the city acquired his collection of about 4700 prehistorical African stone paintings, kept at the University's institute of ethnology, which was named the Frobenius Institute in his honour in 1946.
• The necessary and sufficient conditions for complete integrability of a Pfaffian system are given by the Frobenius theorem.
• In general, the Frobenius method gives two independent solutions provided that the indicial equation's roots are not separated by an integer (including zero).
• On the other hand, this makes the Frobenius normal form rather different from other normal forms that do depend on factoring the characteristic polynomial, notably the diagonal form (if A is diagonalizable) or more generally the Jordan normal form (if the characteristic polynomial splits into linear factors).
• Furthermore, in the abelian case, associating an unramified prime of K to its Frobenius and extending multiplicatively defines a homomorphism from the group of unramified ideals of K into G.

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