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
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