# About the basis of a quotient space

## Main Question or Discussion Point

Notations:
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 {s1, ... , sk} 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, let R2 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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