Field
The next simplest example is the field F itself. Vector addition is just field addition and scalar multiplication is just field multiplication. Any non-zero element of F serves as a basis so F is a 1-dimensional vector space over itself.
The field is a rather special vector space; in fact it is the simplest example of a commutative algebra over F. Also, F has just two subspaces: {0} and F itself.
Read more about this topic: Examples Of Vector Spaces
Famous quotes containing the word field:
“I see a girl dragged by the wrists
Across a dazzling field of snow,
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Once it would not be so....”
—Philip Larkin (1922–1986)
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“Wynken and Blynken are two little eyes,
And Nod is a little head,
And the wooden shoe that sailed the skies
Is a wee one’s trundle-bed.”
—Eugene Field (1850–1895)