A shield matrix was the series of physical components responsible for the generation and projection of a vessel's protective energy screens.
In 2154, Commander Shran noticed that the shield matrix of an attacking Andorian battle cruiser was of a completely unfamiliar configuration. Shran and the crew of Enterprise NX-01 eventually came to realize that the ship was not Andorian at all, but rather a Romulan ship using holographic camouflage. (ENT: "Babel One")
In 2375, as part of their plot to obtain a Borg transwarp coil, the crew of the USS Voyager boarded a Borg sphere and proceeded to the vessel's shield matrix. Ensign Harry Kim subsequently placed spatial charges around the primary shield generator, detonating them in order to allow the Voyager crew to obtain a transporter lock on the coil. (VOY: "Dark Frontier")
The next year, while attempting to break free from a Borg tractor beam, Captain Janeway noticed that the beam being generated by the Borg cube drew power from the same grid as its shield matrix. Using Voyager's deflector to send a feedback pulse along the tractor beam, Janeway managed to disrupt the cube's shields and beam aboard several crewmembers who were being held by a group of adolescent drones. (VOY: "Collective")
In 2377, the Voyager crew was able to tap into the shield matrix of an attacking Lokirrim warship, using a command authorization covertly supplied to the crew by The Doctor, who was being held captive aboard the warship. (VOY: "Body and Soul")