Matrices and bases

  • Thread starter Gramsci
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  • #1
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I'm having some trouble understanding basis and how they relate to transformation matrices.

Homework Statement


Let e_1,e_2,e_3,e_4 be a basis in a four dimensional vector space V. Suppose that the linear transformation F on V has the matrix representation:
[1 0 2 1;-1 2 1 3;1 2 5 5;2 -2 1 -2] (Matlab-notation).
Find F:s matrix representation in the basis f_1= e_1-2e_2+e_4 , f_2=3e_2-e_3-e_4, f_3=e_3+e_4, f_4=2e_4.


Homework Equations


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The Attempt at a Solution


I thought of using B^(-1)AB (B is the basis A the transformation matrix), but I can't invert our basis here. What should I do?
 

Answers and Replies

  • #2
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The e's represent the usual euclidian base e1 = (1,0,0,0), e2=(0,1,0,0) etc...
 
  • #3
vela
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I'm having some trouble understanding basis and how they relate to transformation matrices.

Homework Statement


Let e_1,e_2,e_3,e_4 be a basis in a four dimensional vector space V. Suppose that the linear transformation F on V has the matrix representation:
[1 0 2 1;-1 2 1 3;1 2 5 5;2 -2 1 -2] (Matlab-notation).
Find F:s matrix representation in the basis f_1= e_1-2e_2+e_4 , f_2=3e_2-e_3-e_4, f_3=e_3+e_4, f_4=2e_4.

The Attempt at a Solution


I thought of using B^(-1)AB (B is the basis A the transformation matrix), but I can't invert our basis here. What should I do?
That's what you want to do, but I think you're trying to invert the wrong matrix.
 

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