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)...

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

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...

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...

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

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....

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...

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...

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^{*}...

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

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...

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 +...

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

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...

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...

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...

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

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

convex normal neighborhood U is a normal neighborhood of every p in U. The existence of these sort 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...

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

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...

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

to "positive basis", which occurs when the current spot price exceeds the price of the future.: 22  The opposite market condition to normal backwardation...

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...

discovery. The tangent, normal, and binormal unit vectors, often called T, N, and B, or collectively the Frenet–Serret basis (or TNB basis), together form an...