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Definition of dimension of a vector space (or subspace)
If a vector space has dimension n
Every basis for a vector space contains the same number of elements
Definition of dimension of a vector space (or subspace) being finite or infinite
The dimension of a subspace is less than or equal to the dimension of the whole space
If two finite dimensional subspaces have the same dimension and one is contained in the other
A set of vectors containing more elements than the dimension of the space must be linearly dependent
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Dimension
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If two finite dimensional subspaces have the same dimension and one is contained in the other
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