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Jets provides familiar matrix-vector syntax without forming matrices. Instead, the action of the matrix and its adjoint applied to vectors is specified using Julia methods. In addition, Jets provides a framework for nonlinear functions and their linearization. The main construct in this package is a jet and is loosely based on its mathematical namesake (https://en.wikipedia.org/wiki/Jet_(mathematics)). In particular, a jet describes a function and its linearization at some point in its domain.