The Holomatrix is the programming code for holographic software such as; holonovels, the Emergency Medical Hologram, and other holoprograms. (TNG, DS9, VOY)
It is also a term used to refer to the hologrid, the systems used to project holographic images on the holodeck.
By the 29th century the term holomatrix was used to refer to that century's equivalent to a holodeck. Braxton had Seven of Nine report to Holo-Matrix 1 aboard the USS Relativity to run a simulation of her mission aboard USS Voyager to remove a temporal disruptor. (VOY: "Relativity")