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Definition LT. Linear Transformation. A linear transformation, T : U â V , is a function that carries elements of the vector space U (called the domain) to the vector space V (called the codomain), and which has two additional properties.
Definition IVLT Invertible Linear Transformations. Suppose that $\ltdefn{T}{U}{V}$ is a linear transformation. If there is a function $\ltdefn{S}{V}{U}$ such that \begin{align*} \compose{S}{T}&=I_U & \compose{T}{S}&=I_V \end{align*} then $T$ is invertible.heorem ICLT Inverse of a Composition of Linear Transformations. Suppose that $\ltdefn{T}{U}{V}$ and $\ltdefn{S}{V}{W}$ are invertible linear transformations. Then $\compose{S}{T}$ is invertible and $\ltinverse{\left(\compose{S}{T}\right)}=\compose{\ltinverse{T}}{\ltinverse{S}}$.