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## Main Question or Discussion Point

Just like the title says, what is a dual vector. I am reviewing Panton's "Incompressible Flow", Chapter 3, and a brief section is dedicated to calculating the dual vector and its inverse. Unfortunately, along with many other concepts in this book (if you're into fluids mechanics I don't recommend this text), Panton fails to give an in-depth discussion regarding the motivation, purpose or derivation of a dual vectors. In other words, I would like to know what purpose the dual vector serves, why would one want to use it and if possible an "intuitive" derivation/proof. My background in abstract mathematics is informal and limited so go easy!

Side Note: After doing some research I acquired information on dual spaces, which seems to be a space that when a vector field from its original space multiplied by its corresponding field in the dual space yields the Kronecker delta. Would the dual vector be just one vector from this vector field? That still doesn't answer why one would want to make use of it.

Thanks

Side Note: After doing some research I acquired information on dual spaces, which seems to be a space that when a vector field from its original space multiplied by its corresponding field in the dual space yields the Kronecker delta. Would the dual vector be just one vector from this vector field? That still doesn't answer why one would want to make use of it.

Thanks