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Images. If if is the field (r of real numbers, v is called a real vector space; The number of vectors) of a basis of v over its base field.
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Finite dimensional vector spaces are not finite dimensional hilbert spaces. I kind of think that one should use the fact that any two norms on the finite vector space are equivalent, but i don't know how to proceed forward. A great rigorous intro to linear algebra.
Here are some theorems which shouldn't be too hard to prove.
In mathematics, the dimension of a vector space v is the cardinality (i.e. Now, r is certainly a vector space. The relation between a vector space v and the underlying field jf is usually described by saying that ? Note that the dimension of a linear space of column vectors having entries can be less than , as shown by the following example.
