In group theory, a discipline within modern algebra, an element of a group is called a real element of if it belongs to the same conjugacy class as its inverse , that is, if there is a in with , where is defined as .[1] An element of a group is called strongly real if there is an involution with .[2]
An element of a group is real if and only if for all representations of , the trace of the corresponding matrix is a real number. In other words, an element of a group is real if and only if is a real number for all characters of .[3]
A group with every element real is called an ambivalent group. Every ambivalent group has a real character table. The symmetric group of any degree is ambivalent.
discipline within modern algebra, an element x {\displaystyle x} of a group G {\displaystyle G} is called a realelement of G {\displaystyle G} if it belongs...
identity element of the addition of real numbers. This concept is used in algebraic structures such as groups and rings. The term identity element is often...
greatest element of S . {\displaystyle S.} For example, consider the set of negative real numbers (excluding zero). This set has no greatest element, since...
The finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical...
The Fifth Element is a 1997 English-language French science fiction action film conceived and directed by Luc Besson, as well as co-written by Besson...
in order theory, the greatest element of a subset S {\displaystyle S} of a partially ordered set (poset) is an element of S {\displaystyle S} that is...
correspond to real components, the representation can be in the form of a schematic diagram or circuit diagram. This is called a lumped-element circuit model...
marketed as "Real Time 4WD". The Element has a towing capacity of 680 kg, or 1500 lbs and a gross weight of 4450 lbs (2018 kg). In 2007, the Element won the...
element: phosphorus. List of fictional elements, materials, isotopes and subatomic particles Materials science in science fiction Dysprosium, a real element...
hypercomplex number is a traditional term for an element of a finite-dimensional unital algebra over the field of real numbers. The study of hypercomplex numbers...
data element is an atomic unit of data that has precise meaning or precise semantics. A data element has: An identification such as a data element name...
sometimes referred, in local languages, to "air" as "wind", and the fifth element as "space". These different cultures and even individual philosophers had...
Extended periodic table Element 119 (Uue, marked here) in period 8 (row 8) marks the start of theorisations. An extended periodic table theorizes about...
An HTML element is a type of HTML (HyperText Markup Language) document component, one of several types of HTML nodes (there are also text nodes, comment...
Austrian physicist who was one of those responsible for the discovery of the element protactinium and would jointly confirm that nuclear fission was a replicable...
unable to continue this work to its logical conclusion and identify the realelement 93. They identified ten different half lives, with varying degrees of...
Lois Lane. The mineral known as kryptonite, not to be confused with the realelement krypton, was first officially introduced in the radio serial The Adventures...
absorbing element with any element of the set is the absorbing element itself. In semigroup theory, the absorbing element is called a zero element because...
inverse element generalises the concepts of opposite (−x) and reciprocal (1/x) of numbers. Given an operation denoted here ∗, and an identity element denoted...
mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted i, called the imaginary unit...
|b|=(b^{*}b)^{\frac {1}{2}}} . For every real number α ≥ 0 {\displaystyle \alpha \geq 0} there is a positive element a α ∈ A + {\displaystyle a^{\alpha }\in...
Control Service Element) ROSE (Remote Operation Service Element) CCR (Commitment Concurrency and Recovery) RTSE (Reliable Transfer Service Element) The specific...
{\displaystyle L} is a transitive class and the interpretation uses the realelement relationship, so it is well-founded. L {\displaystyle L} is an inner...
nonzero element by zero. It has cyclic order described by a separation relation. The long real line pastes together ℵ1* + ℵ1 copies of the real line plus...
relates every element of X {\displaystyle X} to itself. An example of a reflexive relation is the relation "is equal to" on the set of real numbers, since...
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