Difference between revisions of "Linear group"
Jump to navigation
Jump to search
m |
(correct definition) |
||
| Line 1: | Line 1: | ||
| − | The '''general linear group''' over a field <math>X \ </math>, written <math>\mathbb{GL}(X,n) \ </math> is the set of all <math>n \times n \ </math> matrices with elements from the field <math>X \ </math>, under the operation of matrix multiplication. | + | The '''general linear group''' over a field <math>X \ </math>, written <math>\mathbb{GL}(X,n) \ </math> is the set of all invertible <math>n \times n \ </math> matrices with elements from the field <math>X \ </math>, under the operation of matrix multiplication. |
The '''special linear group''' is the subgroup of the general linear group consisting of matrices with determinant 1. | The '''special linear group''' is the subgroup of the general linear group consisting of matrices with determinant 1. | ||
Revision as of 23:40, November 24, 2009
The general linear group over a field , written is the set of all invertible matrices with elements from the field , under the operation of matrix multiplication.
The special linear group is the subgroup of the general linear group consisting of matrices with determinant 1.