Editing Quotient space (linear algebra) (section)

=== Examples ===
Let ''C''[0,1] denote the Banach space of [[continuous function|continuous]] real-valued [[function (mathematics)|functions]] on the [[interval (mathematics)|interval]] [0,1] with the [[sup norm]]. Denote the subspace of all functions ''f'' &isin; ''C''[0,1] with ''f''(0) = 0 by ''M''. Then the equivalence class of some function ''g'' is determined by its value at 0, and the quotient space {{nowrap|''C''[0,1]/''M''}} is isomorphic to '''R'''.

If ''X'' is a [[Hilbert space]], then the quotient space ''X''/''M'' is isomorphic to the [[Hilbert space#Orthogonal complements and projections|orthogonal complement]] of ''M''.