  The transmission matrix is a unique tool to control light through a
scattering medium. A monochromatic transmission matrix does not allow temporal
control of broadband light. Conversely, measuring multiple transmission
matrices with spectral resolution allows fine temporal control when a pulse is
temporally broadened upon multiple scattering, but requires very long
measurement time. Here, we show that a single linear operator, measured for a
broadband pulse with a co-propagating reference, naturally allows for spatial
focusing, and interestingly generates a two-fold temporal recompression at the
focus, compared with the natural temporal broadening. This is particularly
relevant for non-linear imaging techniques in biological tissues.
