Suppose that 
is a vector space over the field
of complex or real numbers.
Then the set of all linear functionals on 
forms a vector space called the algebraic conjugate
space 
of 
.
It is known that 
has dimension 
if and only if 
does (Kreyszig 1978).
Algebraic Conjugate Space
See also
Dual Vector SpaceThis entry contributed by Mohammad Sal Moslehian
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References
Kreyszig, E. Introductory Functional Analysis with Applications. New York: Wiley, 1978.Referenced on Wolfram|Alpha
Algebraic Conjugate SpaceCite this as:
Moslehian, Mohammad Sal. "Algebraic Conjugate Space." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/AlgebraicConjugateSpace.html