In geometry the change of variable,(adsbygoogle = window.adsbygoogle || []).push({});

[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^{B}_{B'}have such a representation with B and B'? Why wouldn't it be^{B'}_{B}?

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# Change of Coordinate Matrix

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