Editing Vector space (section)

===Coordinate space===
The simplest example of a vector space over a field {{math|''F''}} is the field {{math|''F''}} itself with its addition viewed as vector addition and its multiplication viewed as scalar multiplication. More generally, all [[tuple|{{math|''n''}}-tuples]] (sequences of length {{math|''n''}}) 
<math display=block>(a_1, a_2, \dots, a_n)</math>
of elements {{math|''a''<sub>''i''</sub>}} of {{math|''F''}} form a vector space that is usually denoted {{math|''F''<sup>''n''</sup>}} and called a '''coordinate space'''.{{sfn|Lang|1987|loc = ch. I.1}} 
The case {{math|1=''n'' = 1}} is the above-mentioned simplest example, in which the field {{math|''F''}} is also regarded as a vector space over itself. The case {{math|1=''F'' = '''R'''}} and {{math|1=''n'' = 2}} (so '''R'''<sup>2</sup>) reduces to the previous example.