rifat Messages 3 Reaction score 0 Thread starter Apr 18, 2008 #1 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}?"
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}?"
Dick Science Advisor Homework Helper Messages 26,254 Reaction score 623 Apr 18, 2008 #2 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?
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?