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Example II:

Let M be the set of all (m×n) matrices, with complex numbers as entries. Let C be the field of complex numbers. Then if

where p_ij is in C.

Define vector addition in M:

Define scalar multiplication:

Then M is a vector space over C and we denote this as C^m×n.

So Example I would be denoted R^1×n, or more simply, Rⁿ.

In analysis, many function sets have the structure of a vector space. In analysis, a vector space is called a linear space.

See also: Vector space

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Topics: Vector Space Example 2, Vector Space, Vector Space Example 1...

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