A linear map \(\LinMap{L}\from \VSpc{V}\to \VSpc{W}\) of subvector spaces of \(\RNrSpc{k}\) is called invertible or is an isomorphism if there exists a linear map \(\LinMap{M}\from \VSpc{W}\to \VSpc{V}\) such that

\[\LinMap{M}\Comp \LinMap{L} = \IdMapOn{V} \quad\text{and}\quad \LinMap{L}\Comp \LinMap{M} = \IdMapOn{W}\]

In this case we call \(\LinMap{M}\) the inverse of \(\LinMap{L}\) and write \(\LinMap{M}=\LinMap{L}^{-1}\).