Warp matrix engineering, also called warp mechanics, (TV: The Leisure Hive) was a form of temporal mechanics (PROSE: Doctor Who and the Leisure Hive) that enabled manipulation of the physical universe to create dimensional transcendence, and was a cornerstone of Time Lord science. (PROSE: First Frontier)
The Seventh Doctor explained the principle to Marion Davison in 1957, who remarked that it was like something out of Future Boy.
The universe is basically infinite, because it has no exterior boundaries. At the same time, because any finite number divided by infinity is zero, then although the universe has eleven dimensions it is also a single point with no dimensions at all. Since there is nothing outside then nothing can enter or leave, and all that can happen is that the state of its contents can change. [...] Now, because the universe is an infinite single point there's no reason why you can't go from one point to another instantly on account of the fact that you aren't actually moving because you're staying put in the one point that is the universe. Since time is just another dimension also divided by infinity, the same principle applies. All you have to know is how to get down to the basic building blocks of reality. Numbers. The essence of matter is structure, and the essence of structure is mathematics. When your physicists get around to investigating quantum mechanics and sub-nuclear physics, they invariably find that even the smallest particle is always made of something even smaller. There always follows a point as which that something smaller is too small to have a physical existence and can only exist as a mathematical concept in the mind of the observer. All you have to do is manipulate those concepts to effect changes in the physical universe - turn parts inside out as TARDISes, warp space and time, hop between dimensions, all that sort of thing.
Gallifrey had abandoned tachyonics when they developed warp matrix engineering, (TV: The Leisure Hive) "ages" before 2290, (PROSE: Doctor Who and the Leisure Hive)