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...

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

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...

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

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....

using the normal basis representation of elements, however, the algorithm is generic and can be used for other bases, such as the polynomial basis. It can...

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...

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...

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^{*}...

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 +...

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

of a completely dry material, as opposed to the wet basis ratio of water to a material under normal conditions that contains a measurable amount of moisture...

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...

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...

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...

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...

ln(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 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...

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...

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

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...

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...

associated with the columns of a matrix, and A is said to be a basis of L. Because the Hermite normal form is unique, it can be used to answer many questions...

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

can be diagonalized (that is, represented as a diagonal matrix in some basis). This is extremely useful because computations involving a diagonalizable...

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

people still come to this mosque to pray and visit the mausoleum on a normal basis. Although non-Muslims are not allowed into the building, the structure...

linear map under two (possibly) different bases, with P being the change-of-basis matrix. A transformation A ↦ P−1AP is called a similarity transformation...