A) Given the following transformation which is called the Lorentz Transformation

Question

A) Given the following transformation which is called the Lorentz Transformation    

Z= [ 5/4 3/4]

       [ 3/4 3/4]

If you pick the corner vertices of a square centered at the origin

[ 1 ]  , [ 1 ] , [ -1 ] , [ -1 ]

[  1 ]  [ -1 ]  [  1  ]   [ -1   ]

and L2 maps this square from lR^2 into lR^2 then what is the shape of the square under the transformation? Where did each of these vertices get mapped to?

B) In the previous problem what is the area of the original square and what is the area of the new object under the transformation?

C) What is the determinant of matrix L2 and is matrix L2 invertible. If it is invertible then find the inverse?

D) If L2 is invertible what does this tell you about the dimension of the Null Space of matrix and is the corresponding linear transformation one-to-one or not?

Explanation / Answer

HI, I have posted the links for the pics with the solutions, the first image countains solutions for A,B and second one for C,D. Let me know if you have any doubts or concerns with the solution.

http://tinypic.com/r/j6u6x0/5

http://tinypic.com/r/2viidg9/5

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