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V denotes a vector space

S denotes a subspace of V

V/S denotes a quotient space

V\S denotes the complement of S in V

Question:

If {s_{1}, ... , s_{k}} is a basis for S, how to find a basis for V/S?

I realize that the basis of V\S may determine the basis of V/S, but I don't know how to formulate it. For example, letR^{2}be the Cartesian plane V^{,}with basis {(1,0),(0,1)}, the diagonal is a subspace S^{,}whose basis is {(1,1)}, then how to formulate the basis of V^{,}\S^{,}?

Thanks for any help!

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# About the basis of a quotient space

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