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Memory Alpha

A positronic matrix was a significant part of an android's positronic brain, but could also be adapted for use in conjunction with a humanoid's brain.

When Data created his "daughter" Lal in 2366, during her development he observed some quantum variations, notably her use of contractions. Because her neural net was identical to Data's, he began to maintain records on her positronic matrix activity, behavioral norms, and verbal patterns. (TNG: "The Offspring") Lal subsequently "died" as a result of having an unstable positronic matrix. (TNG: "Inheritance")

During the Ktarians' attempt to overtake the Federation, and the resulting attempt to take over the USS Enterprise-D, Doctor Beverly Crusher managed to deactivate Data by disconnecting his positronic matrix. (TNG: "The Game")

Commander William T. Riker was aware that sufficiently large amounts of radiation would ionize Data's positronic matrix, which would kill him. (TNG: "The Quality of Life")

After Lore began leading a rogue group of Borg, he was able to capture Data to assist him in his conquests. During their time together, Lore controlled Data by means of transmitting a carrier wave which affected Data's positronic matrix. (TNG: "Descent, Part II")

Juliana Tainer, Data's "mother", had been injured during an attack by the Crystalline Entity. In an attempt to save her life, Noonian Soong was able to successfully transfer her memories into a positronic matrix, after having perfected his synaptic scanning technique. Shortly thereafter Juliana died, but Noonian was able to save her by making her into an android. Years later, Juliana lost consciousness following an accident. Before the real reason was revealed, it was suggested that perhaps her positronic matrix may have experienced a cascade anomaly, as she should have otherwise not experienced such trauma. (TNG: "Inheritance")

In 2370, Data took part in a mission to Barkon IV to locate a crashed Federation probe, and collect the radioactive fragments it had dispersed. As Data was attempting to download the sensor logs from the probe computer, the probe experienced a power surge, which overloaded Data's positronic matrix, giving him amnesia. (TNG: "Thine Own Self")

Following a plasma explosion aboard a Bajoran transport, it was suggested and agreed upon that Bareil Antos, who had suffered severe brain damage, have half of his brain replaced with a positronic matrix. When the remaining half began fail, however, this was not chosen as to not take away his last shred of humanity. (DS9: "Life Support")

During a confrontation with the Son'a, Data suffered damage resulting in a phase variance in his positronic matrix. The Ba'ku, who were familiar with such technology, were unable to make the necessary repairs. (Star Trek: Insurrection)

Prior to Data's death, he successfully integrated his memory engrams into B-4's positronic matrix, in an attempt to give him Data's memories and abilities resulting in a more complete individual. (Star Trek Nemesis)

Mendaxic neurosclerosis was a very rare and fatal disease caused by a silicon-based virus, but could easily be cured by culturing infected cells in an active positronic matrix. (PIC: "Nepenthe")