mathematics, specifically the algebraic theory of fields, a normal basis is a special kind of basis for Galois extensions of finite degree, characterised as...

Gröbner basis Hilbert's basis theorem Generating set of a group Base (topology) Change of basis Greedoid Normal basis Polynomial basis Radial basis function...

episode of the TV series Normal (geometry), an object such as a line or vector that is perpendicular to a given object Normal basis (of a Galois extension)...

GF(2m) using the normal basis representation of elements, however, it is generic and can be used for other bases, such as the polynomial basis. It can also...

{\displaystyle AM=MJ} . Canonical form Change of basis Normal basis Normal form (disambiguation) Polynomial basis Bronson (1970, p. 196) Lusztig (1990) Kashiwara...

respect to a basis for which the operator takes its Jordan normal form. The diagonal form for diagonalizable matrices, for instance normal matrices, is...

In probability theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued...

zero. A dual basis () is not a concrete basis like the polynomial basis or the normal basis; rather it provides a way of using a second basis for computations...

equivalent to the existence of a normal integral basis, i.e. of α in OL such that its conjugate elements under G give a free basis for OL over OK. This is an...

L is a finite extension of K, then its normal closure is also a finite extension. Galois extension Normal basis Lang 2002, p. 237, Theorem 3.3, NOR 3....

the content of the normal basis theorem, a normal basis being an element x of L such that the g(x) for g in G are a vector space basis for L over K. Such...

is the starting point of Gröbner basis theory. The definition of the reduction shows immediately that, if h is a normal form of f by G, one has f = h +...

earthquakes and volcanoes. Insurance adjusters analyze external risks on a normal basis. Measuring risks of the environment is common practice throughout insurance...

1007/BF01472227 Stauffer, Ruth (July 1936), "The Construction of a Normal Basis in a Separable Normal Extension Field", American Journal of Mathematics, 58 (3):...

X has a normal distribution. Equivalently, if Y has a normal distribution, then the exponential function of Y, X = exp(Y), has a log-normal distribution...

In U.S. constitutional law, rational basis review is the normal standard of review that courts apply when considering constitutional questions, including...

square matrix A is normal if it commutes with its conjugate transpose A*: A  normal ⟺ A ∗ A = A A ∗ . {\displaystyle A{\text{ normal}}\iff A^{*}A=AA^{*}...

others look quite different (for instance, using matrices). Using a normal basis may have advantages in some contexts. When the prime is 2, it is conventional...

("contango") or discounts ("backwardation"). Basis trades are generally considered low-risk under normal market conditions, but they can be subject to...

normal to the plane in the z direction: e 0 = e z {\displaystyle \mathbf {e} _{0}=\mathbf {e} _{z}} The inverse relations are: While giving a basis in...

In linear algebra, the Frobenius normal form or rational canonical form of a square matrix A with entries in a field F is a canonical form for matrices...

In geometry, a normal is an object (e.g. a line, ray, or vector) that is perpendicular to a given object. For example, the normal line to a plane curve...

convex normal neighborhood U is a normal neighborhood of every p in U. The existence of these sorts of open neighborhoods (they form a topological basis) has...

widely used until decades later. The term "normal saline" itself appears to have little historical basis, except for studies done in 1882–83 by Dutch...

Covers an exceptional case of Kummer theory, in characteristic p. Normal basis A basis in the vector space sense of L over K, on which the Galois group...

theorem is a result on cyclotomic fields, characterising those with a normal integral basis. More generally, it applies to any finite abelian extension of Q...

different voltages or frequencies.) The grids may be synchronised on a normal basis, but events may interrupt synchronisation. This is not a problem for...

facts which should not be a sufficient ground for departing from the normal basis on which damages are awarded: the fact that the breach was cynical and...

in algebraic number theory and the arithmetic of elliptic curves. The normal basis theorem implies that the first cohomology group of the additive group...

derivatives can be used as a basis of the tangent spaces at every point. In order to find the perturbation in the normal the tangent space must be correctly...