A translation matrix was a data construct that facilitated the conversion of symbols and sounds from one language to another. It was a major component of communication systems and devices such as the universal translator.

Translation matrices were included in the Friendship 1 probe, launched in 2067. (VOY: "Friendship One")

In 2155 of the mirror universe, Hoshi Sato had to enable the translation matrix in order for Jonathan Archer to communicate with the Gorn slave master Slar. (ENT: "In a Mirror, Darkly, Part II")

Hoshi Sato invented the linguacode translation matrix sometime in the late 2160s. (ENT: "In a Mirror, Darkly, Part II")

Due to its unique syntax and grammatical structure, the spoken language of the Skrreeans was difficult for the universal translator to lock onto. Therefore, it took some time to establish a translation matrix. (DS9: "Sanctuary")

The Emergency Medical Hologram has a built-in translation matrix. In 2375, The Doctor's translation matrix allowed him to understand the duotronic algorithm communication of a Druoda series 5 long-range tactical armor unit. (VOY: "Warhead")

In early 2376, the crew of the USS Voyager unsuccessfully attempted to design a translation matrix that would allow communication with the nucleogenic lifeforms attacking the ship. (VOY: "Equinox, Part II")

One of the items offered by Abaddon in 2376 was a slightly dated translation matrix. (VOY: "Alice")

Later that year, the Voyager crew used a translation matrix to interpret the symbols on the Tarakis memorial monument. (VOY: "Memorial")

The translation matrix may involve the use of the translation algorithm.

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