Standard (mathematics)

In mathematics, the word standard is often used in its non-technical sense to indicate the "normally" or "most frequently" used of several options. Words with a similar, but usually more formal and more technical meaning are: normal, natural, canonical. Thus there may be, for instance,
 * a "standard" symbol that is usually (but not necessarily always) used, or
 * a "standard" way to write an equation that need not be considered as a normal form.

Some very common examples for the use of the word "standard" are:


 * The standard basis in d-dimensional real or complex vector spaces (or, more generally, in any d-dimensional vector space Kd over a field K)
 * is the basis formed by the d d-tuples
 * $$(1,0,\dots,0),\ (0,1,0,\dots,0), \cdots, (0,\dots,0,1,0),\ (0,\dots,0,1) $$


 * In set theory, standard model of the natural numbers usually refers to the the set $$\mathbb N$$ constructed inductively from the empty set.


 * The term standard (natural, real, complex, etc.) numbers is used to distinguish the usually used numbers from their nonstandard counterparts.


 * In statistics the standard deviation is the most commonly used measure of variation.


 * In mathematical physics there is a well-known standard model of particle physics.