I am not really sure if I am doing this problem correctly if you could point out any errors that would be great.(adsbygoogle = window.adsbygoogle || []).push({});

The problem: The coordinates of a hyperbolic system (u,v,z) are related to a set of cartesian coordinates (x,y,z) by the equations

u=x^2-y^2

v=2xy

z=z

Determine the transformation matrix [a] that takes the cartesian componets of a vector to the hyperbolic components.

What I did:

the transformation matrix is given by a_ij = dx'_ij/dx_ij, where dx'/dx are partial derivatives and x' corresponds to u,v,z.

giving a matrix of | 2x -2y 0 | | x -y 0|

| y x 0 | = |y x 0|

|0 0 1 | |0 0 1 |

After dividing first two rows by 2.

I know that [a][a]^T = [1]

for [a][a]^T = | ( x^2+y^2) 0 0 |

| |

| 0 (x^2+y^2) 0|

| |

| 0 0 1|

which can only equal the identity if x^2+y^2=1

I was wandering if this looks ok

thanks

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# Hyperbolic matrix transform

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