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let's E be a vector space, e_ {i} be a basis of E, b_ {a} an element of E then

b_ {a} = b_ {a} ^ {i} e_ {i}.

I want to define a family of vectors {t_ {i}}, that lives on E , (how to choose this family already, it must not be a base or even generator?!) And I want to write b_ {a} in function of {t_ {i}}?!

I hope you can help me.

Good day :)......