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Just curious as to whether Gl(n,R) (aka invertible nxn matrices over R), is

finitely-generated by the shear maps : add a k-multiple of one row to another row.

It seems clear that i) shear maps preserve invertibility (actually preserve determinant),

and it would seem we could generate any matrix this way. Is this correct?

Also: are there results for general rings Z, i.e., for a generating set for Gl(n,Z);

Z any ring?

Thanks.

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# Generators for Gl(n,R)?

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