What is the dimension of the dual space V* of a finite-dimensional vector space V?
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The same as V
The dual space V* consists of all linear functionals on V. For finite-dimensional spaces, V and V* are isomorphic, meaning they have the same dimension, though the isomorphism is not 'natural' without an inner product.
Also asked as:
- How does the dimension of a finite-dimensional vector space V compare to the dimension of its dual space V*?