# definition

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• March 10th 2010, 07:40 AM
alexandrabel90
definition
hi

may i know what it means by R ^x where R= real numbers? and what does GL (subscript 2) (R) means?

thanks
• March 10th 2010, 09:36 AM
tonio
Quote:

Originally Posted by alexandrabel90
hi

may i know what it means by R ^x where R= real numbers? and what does GL (subscript 2) (R) means?

thanks

For any field (or even commutative ring) $R\,,\,\,R^{*}:=R\setminus \{0\}\,\,\,(or\,\,\,R^{*}=$ the set of all units in the ring R) , and $GL_2(R)=$ the set of all invertible 2 x 2 matrices with elements in R (or the set of all R-automorphism of the R-module R x R)

Tonio
• March 10th 2010, 10:07 AM
alexandrabel90
then what is the different between GL (subscript 2) (R) and SL(subscript 2) (R)?

THANKS!!!