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- Q1050120 subject Q7485314.
- Q1050120 subject Q8548677.
- Q1050120 abstract "In mathematics, a matrix group is a group G consisting of invertible matrices over some field K, usually fixed in advance, with operations of matrix multiplication and inversion. More generally, one can consider n × n matrices over a commutative ring R. (The size of the matrices is restricted to be finite, as any group can be represented as a group of infinite matrices over any field.) A linear group is an abstract group that is isomorphic to a matrix group over a field K, in other words, admitting a faithful, finite-dimensional representation over K.Any finite group is linear, because it can be realized by permutation matrices using Cayley's theorem. Among infinite groups, linear groups form an interesting and tractable class. Examples of groups that are not linear include all "sufficiently large" groups; for example, the infinite symmetric group of permutations of an infinite set.".
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- Q1050120 wikiPageWikiLink Q7485314.
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- Q1050120 wikiPageWikiLink Q8548677.
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- Q1050120 comment "In mathematics, a matrix group is a group G consisting of invertible matrices over some field K, usually fixed in advance, with operations of matrix multiplication and inversion. More generally, one can consider n × n matrices over a commutative ring R.".
- Q1050120 label "Matrix group".