matrix group

Noun

 * 1)  Any group of invertible matrices over a specified field, with the group operation of matrix multiplication.
 * 2) * 2011, László Babai, Finite Groups and Complexity Theory: From Leningrad to St Petersburg via Las Vegas, Alexander Kulikov, Nikolay Vereshchagin (editors), Computer Science – Theory and Applications: 6th International Computer Symposium, Springer, Lecture Notes in Computer Science 6651, page 162,
 * This paper is a personal account of the author's journey through the evolution of some of these interconnections, culminating in recent definitive results on the matrix group membership problem.
 * 1) * 2014, Peter Sarnak, Notes on thin matrix groups, Emmanuel Breuillard, Hee Oh (editors), Thin Groups and Superstrong Approximation,, page 343,
 * Applications to diophantine problems on orbits of integer matrix groups, the affine sieve, group theory, gonality of curves and Heegaard genus of hyperbolic three manifolds, are given.
 * Applications to diophantine problems on orbits of integer matrix groups, the affine sieve, group theory, gonality of curves and Heegaard genus of hyperbolic three manifolds, are given.

Usage notes
A group isomorphic to a matrix group is called a and is said to be linear. In mathematical terms, for any linear group G, there exist a field K, an integer d and an injective homomorphism from G to (for some n) the general linear group GLn(K) that is a faithful linear representation of dimension d over K. G can be said to be linear of degree d over K.