1. Mar 20, 2010 #1

   jakey

   

   How do we show that, given a matrix $A$, the sign of the determinant is positive or negative depending on the orientation of the rows of A, with respect to the standard orientation of $R^n$?

    

   jakey, Mar 20, 2010
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3. Mar 20, 2010 #2

   quasar987

   

   Science Advisor

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   Isn't that the very definition of "the rows making up the columns of A have the same (res. the opposite) orientation as the standard basis" ?
   
   If not, write the definition of orientation. you're using.

    

   quasar987, Mar 20, 2010
4. Mar 20, 2010 #3

   jakey

   

   If you refer to the attached file, this matix has a positive orientation (and the sign of the determinant is positive) since the direction from (a,b) to (c,d) is counterclockwise, which is the same orientation as R2 (counterclockwise). Thanks!

    

   Attached Files:

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     pic1.jpg

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   jakey, Mar 20, 2010
5. Mar 20, 2010 #4

   quasar987

   

   Science Advisor

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   I was asking that you write out the definition of what it means for a basis of R^2 to have the same (resp. the opposite) orientation as another basis of R^2.
   
   Your little drawing with arrows does not constitute a mathematical definition.

    

   quasar987, Mar 20, 2010

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