- #1
jeff1evesque
- 312
- 0
In geometry the change of variable,
[tex]x = (2 / sqrt(5))x' - (1 / sqrt(5))y'[/tex] (#1)
[tex]y = (1 / sqrt(5))x' + (2 / sqrt(5))y'[/tex] (#2)
can be used to transform the equation [tex] 2x^2 - 4xy + 5y^2 = 1[/tex] into the simpler equation [tex](x')^2 + 6(y')^2 = 1[/tex], in which form it is easily seen to be the equation of an ellipse.
[tex]B and B'[/tex] are the standard ordered basis and new rotated basis respectively
My question:
Why is BB' have such a representation with B and B'? Why wouldn't it be B'B?
[tex]x = (2 / sqrt(5))x' - (1 / sqrt(5))y'[/tex] (#1)
[tex]y = (1 / sqrt(5))x' + (2 / sqrt(5))y'[/tex] (#2)
can be used to transform the equation [tex] 2x^2 - 4xy + 5y^2 = 1[/tex] into the simpler equation [tex](x')^2 + 6(y')^2 = 1[/tex], in which form it is easily seen to be the equation of an ellipse.
[tex]B and B'[/tex] are the standard ordered basis and new rotated basis respectively
My question:
Why is BB' have such a representation with B and B'? Why wouldn't it be B'B?