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In chemistry and atomic physics, the main group is the group of elements (sometimes called the representative elements) whose lightest members are represented by helium, lithium, beryllium, boron, carbon, nitrogen, oxygen, and fluorine as arranged in the periodic table of the elements. The main group includes the elements (except hydrogen ...
Representative elementary volume. Schematic illustration of idealized fiber arrays and their corresponding unit cells. In the theory of composite materials, the representative elementary volume (REV) (also called the representative volume element (RVE) or the unit cell) is the smallest volume over which a measurement can be made that will yield ...
t. e. The periodic table, also known as the periodic table of the elements, is an ordered arrangement of the chemical elements into rows (" periods ") and columns (" groups "). It is an icon of chemistry and is widely used in physics and other sciences. It is a depiction of the periodic law, which states that when the elements are arranged in ...
An equivalence relation on a set is a binary relation on satisfying the three properties: [1] for all (reflexivity), implies for all (symmetry), if and then for all (transitivity). The equivalence class of an element is defined as [2] The word "class" in the term "equivalence class" may generally be considered as a synonym of "set", although ...
v. t. e. In chemistry, a transition metal (or transition element) is a chemical element in the d-block of the periodic table (groups 3 to 12), though the elements of group 12 (and less often group 3) are sometimes excluded. The lanthanide and actinide elements (the f-block) are called inner transition metals and are sometimes considered to be ...
In the of the elements, each column is a group. In chemistry, a group (also known as a family) [1] is a column of elements in the periodic table of the chemical elements. There are 18 numbered groups in the periodic table; the 14 f-block columns, between groups 2 and 3, are not numbered. The elements in a group have similar physical or chemical ...
The term representation of a group is also used in a more general sense to mean any "description" of a group as a group of transformations of some mathematical object. More formally, a "representation" means a homomorphism from the group to the automorphism group of an object. If the object is a vector space we have a linear representation.
Definition. A matrix coefficient (or matrix element) of a linear representation ρ of a group G on a vector space V is a function fv,η on the group, of the type. where v is a vector in V, η is a continuous linear functional on V, and g is an element of G. This function takes scalar values on G. If V is a Hilbert space, then by the Riesz ...