Admitting an inverse. An object that is invertible is referred to as an invertible element in a monoid or a unit ring, or to a map, which admits an inverse map iff it is bijective. In particular, a linear transformation of finite-dimensional vector spaces T:V->W is invertible iff V and W have the same dimension and the column vectors representing the image vectors in W of a basis of V form a nonsingular matrix. Invertibility can be one-sided. By definition, a map f:X->Y is right-invertible iff it admits a right inverse g:Y->X such that f°g = i d_Y. This occurs iff f is surjective. Left invertibility is defined in a similar way and occurs iff f is injective.
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