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Topological and geometric property of matrix algebra |
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| Authors: | Jipu Ma |
| Institution: | 1.Tseng Yuan-Yun Functional Research Center,Harbin Normal University,Harbin,P.R. China |
| Abstract: | Let B(Rn) be the set of all,n×n real matrices,Sr the set of all matrices with rank r,0≤r≤n,and S#r the number of arcwise connected components of Sr.It is well-known that Sn=GL (Rn) is a Lie group and also a smooth hypersurface in B(Rn) with the dimension n×n. |
| Keywords: | matrix algebra acrwise connected component smooth hypersurface(submanifold) generalized inverse dimension of hypersurface MATRIX ALGEBRA PROPERTY dimension Lie group smooth hypersurface number connected components rank real matrices |
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