A dilithium matrix was one of the key components in a warp drive.
When trying to bring the warp engine online, the Takret lieutenant Paltani had difficulties with the dilithium matrix of Enterprise NX-01. (ENT: "The Catwalk")
In 2154, the Augment Malik overloaded the dilithium matrix on his commandeered Klingon Bird-of-Prey to destroy it, rather than allowing his compatriots to be captured. (ENT: "The Augments")
During his time as the chief engineer of the Columbia, Commander Tucker told his engineering crew that the dilithium matrix must be aligned within 0.3 microns, even though the specifications said 0.5. (ENT: "Affliction")
When contemplating a relationship with Lieutenant Jenna D'Sora, Data remarked to Guinan that he found D'Sora somewhat lacking in her understanding of the dilithium matrix. (TNG: "In Theory")
The power systems of an underground Vidiian base on a rogue planetoid ran on an unusual dilithium matrix. This caused false dilithium readings that drew the USS Voyager there in 2371. (VOY: "Phage")
In 2371, USS Voyager's dilithium matrix experienced a microfracture when Lieutenant B'Elanna Torres initiated a shock pulse from the warp core in an attempt to reverse an implosion ring that had enveloped the ship. Ensign Harry Kim was able to seal the fracture and their plan was unsuccessful. (VOY: "Twisted")
In 2372, when its dilithium matrix was destabilized during a battle with a Pralor starship, Voyager was unable to use its warp drive. (VOY: "Prototype")
Later that year, B'Elanna Torres asked Michael Jonas how the dilithium matrix on the class 2 shuttle Cochrane was holding up, shortly before Tom Paris took it to transwarp. (VOY: "Threshold")
In 2373, Neelix suggested that Torres phase lock the plasma injectors to the dilithium matrix, as the plasma flow in the manifold was constricted. She'd already done so. (VOY: "Fair Trade")
In Tuvok's Insurrection Alpha holo-program, a faulty, possibly sabotaged, dilithium matrix prevented Voyager from achieving warp. (VOY: "Worst Case Scenario")
The crew of the USS Equinox completely redesigned the ship's dilithium matrix after being stranded in the Delta Quadrant, allowing them to use the remains of nucleogenic lifeforms to enhance their engines. (VOY: "Equinox")
In 2374, Tom Paris decoupled Voyager's dilithium matrix in an attempt to avert a tachyon-caused warp core breach, to no effect. (VOY: "Day of Honor")
When Voyager was boarded by a member of Species 8472 later that year, B'Elanna Torres ordered the dilithium matrix realigned to a frequency of 3.69. (VOY: "Prey")
The dilithium matrix on the Silver Blood Voyager required constant monitoring due to the constant use of their enhanced warp drive. (VOY: "Course: Oblivion")
In 2376, Voyager had an alignment error in its dilithium matrix. Lyndsay Ballard, recently returned from the Kobali, identified it as a vyk'tiote. (VOY: "Ashes to Ashes")
In The Doctor's 2378 holonovel Photons Be Free, Lieutenant Torrey said she hadn't seen a dilithium matrix so out of alignment since she "served on a Ferengi garbage scow." (VOY: "Author, Author")
It is unclear if dilithium matrix and stabilizer matrix are the same thing.
"Dilithium matrix" may also be another term for the dilithium articulation frame
, the main processing component which contains and focuses the dilithium to produce warp plasma for starship engines.