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Homeomorphism calculation help

  • Thread starter rifat
  • Start date
3
0
How can we show that the set {A in GL(n;R) | det(A)>0} is homeomorphic to the set {A in GL(n;R) | det(A)<0}?"
 

Answers and Replies

Dick
Science Advisor
Homework Helper
26,258
618
If you think of A as a matrix, how about just replacing the first row with the negative of itself? Isn't that an explicit homeomorphism?
 

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