The Amplified Panatropic Computer Net (or Amplified Panatropic Computations) was a section within the domain of the Matrix on Gallifrey, (TV: The Invasion of Time) that cross-checked the data stored within. (AUDIO: The Inquiry) It was what allowed the Matrix Lords to exert a direct control over physical reality, though they also used the Celestial Intervention Agency as living agents for most mundane purposes. (PROSE: The Legacy of Gallifrey)
According to one account, the Matrix was actually originally a part of the APC Net than the other way around, but over the millennia, the Matrix grew to outstrip the APC Net by far until it was the APC Net that was considered a section of the Matrix. (PROSE: Gallifrey: A Rough Guide) The Matrix could also be referred to as the "APC Matrix Net". (PROSE: The Cyber Files)
The APC, like the rest of the Matrix, was composed of trillions of electrochemical cells in a continuous matrix. When a Time Lord died, a brain scan was made at the moment of death and the impulses were transferred to the Matrix. The Net's function was to monitor life in the Capitol and use the combined knowledge and experiences to predict future developments. (TV: The Deadly Assassin) Every Time Lord, living and dead, from Rassilon to the lowest orderlies, had their brain scan entered into the Net, and it was illegal to remove their scan from it. The Garvond fed on these minds. (PROSE: The Dimension Riders)
A brain scan appeared as a floating globe of data, like an iridescent beachball; these were stored in neatly-pixelled rows of white lockers that outlined a dark space. As it was strictly forbidden by the Time Lords to erase a scan, the security systems of the Panatropic Net would slam into action as soon an intruder was pinpointed, inoculation programs taking the form of protectors with holographic helmets and stasers. The Seventh Doctor entered the Net through a bleached white portal, before creating an access tunnel to the dark space and retrieving his scan. Claws of red and green light shot from the locker to try and retrieve it, but he programmed the globe to "escape," where it split open and scattered the pixels. He considered deleting the scan a form of book-burning. (PROSE: Prelude The Dimension Riders)