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this is my first post on this site so please excuse me (and correct me) if i am not posting according to the guidelines.

im studying right now linear transformations and im a bit shaky concerning dual vector spaces.

i understand the definition but am not sure how to apply it. what exactly is the connection between a regular basis and its dual basis?

i know the delta i,j definition, but that requires an intuitive solution, and thats not always an option.

so in short: is the a general algorithm for computing dual basis, under the assumption that the original vector space and a certain basis are known?

thanks