  We report broadband characterization of the propagation of light through a
multiply scattering medium by means of its Multi-Spectral Transmission Matrix.
Using a single spatial light modulator, our approach enables the full control
of both spatial and spectral properties of an ultrashort pulse transmitted
through the medium. We demonstrate spatiotemporal focusing of the pulse at any
arbitrary position and time with any desired spectral shape. Our approach opens
new perspectives for fundamental studies of light-matter interaction in
disordered media, and has potential applications in sensing, coherent control
and imaging.
