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  1. M

    Linear Algebra - Polar decomposition

    First i calculated the eigenvalues: I got (i-\lambda)(-i-\lambda)+1, so \lambda_{1,2}=+-\sqrt{2}i Is it correct to go on on like this: \lambda_{1}a+b=\sqrt{\lambda_{1}} \lambda_{2}a+b=\sqrt{\lambda_{2}} After calculating a and b, we plug it into f(x) = ax+b --> f(A^{*}A)=a(A^{*}A)+bI Then...
  2. M

    Linear Algebra 2 - Representing Matrix

    oh man yes sure thx again ^^
  3. M

    Linear Algebra 2 - Representing Matrix

    hmm, ok but why ist L(x) = x+1? --> p(x) = x if its a constant function and p(x)=x, shouldnt be P(x+1)=x too???
  4. M

    Linear Algebra 2 - Representing Matrix

    Should it be like that: If p(x) =1 then, q(x) = p(x+1) = p(x)+p(1) = 1 + 1 = 2, so L[1]= 2!?
  5. M

    Square root of a Matrix

    Hey i just tried to calcuculate the eigenvectors. But i cant get a sol. The result is always = 0. ?? Edit: Forget it, using the way with a and b, i was able to solve it correct ^^ (without any eigenvectors)
  6. M

    Linear Algebra - Change of Bases

    Cool :) Thx jbunniii
  7. M

    Linear Algebra - Representing Matrix

    yeah its good thx mate!!! ;)
  8. M

    Linear Algebra 2 - Representing Matrix

    :D:D cool thx alooooot
  9. M

    Linear Algebra 2 - Representing Matrix

    ahh ok so if u change this fpr L(x^2) --> 1 2 1 matrix: 1 1 1 0 1 2 0 0 1 correct? ^^
  10. M

    Linear Algebra 2 - Representing Matrix

    and then for L(1) --> 1 0 0 L(x) --> 1 1 0 L(x^2) --> 1 0 1 So my matrix would be 1 1 1 0 1 0 0 0 1 ??
  11. M

    Linear Algebra 2 - Representing Matrix

    So i get then L(1) = 1 L(x) = x+1 L(x^2)=x^2+1 ?
  12. M

    Linear Algebra - Change of Bases

    Coool thx a lot, easy this way. :D
  13. M

    Linear Algebra 2 - Representing Matrix

    L(p)=q(p)=p(x+1)? wie kommst du da auf L(x)=1+x? Was hast du denn dann für L(1)?
  14. M

    Linear Algebra 2 - Representing Matrix

    But so i get for L(x) = x^2 + x, L(x^2)=x^3 + x^2 So should i choose a new basis, for example {1+x,x^2,x^3} to get the repr matrix?
  15. M

    Linear Algebra - Change of Bases

    the i get as matrix: 4/sqrt(2) 3/sqrt(2) 2/sqrt(2) 1/sqrt(2) correct?
  16. M

    Linear Algebra - Change of Bases

    Is [text]K_{S,B1}[/tex] not the same as B1? And the same for B2? So i calculate the inverste and multply them and then im finished?
  17. M

    Linear Algebra 2 - Representing Matrix

    So this A is the representing matrix? But what does then Ap=q mean? Or how can i calculate L for 1, x and x^2?
  18. M

    Linear Algebra - Change of Bases

    So i should calculate the change of base matrix for B1 to S and the inverse of the change of base matrix for B2 to S coordinates? And multiply this to get my result? Ok i ll try to find out how to calculate the change of base matrix ^^ Thx
  19. M

    Linear Algebra - Representing Matrix

    Thx!!!!!!!!!!!!!!!!!! then i get for: L(x+x^2)=1+2x+x(x+^2)= 1 +2x+x^2+x^3 L(1+x^2)=2x+x(1+x^2)=3x+x^3 You said: write those three output polynomials in terms of the second basis. so if i did this correct i get for 1+x --> 1 0 1 0 x+x^2 --> 0 1 1 1 1+x^2 --> -1 3 0 1 so my matrix is...
  20. M

    Linear Algebra - Change of Bases

    No, i dont even know what K is supposed to be...
  21. M

    Linear Algebra 2 - Representing Matrix

    Sry, this will be the last question^^ Its a similiar to the problem i ve postet before. Maybe if i can solve the first problem i can solve this to. But what i dont understand is that notation. I ve circled it with a red line. Does anyone know what this means? Thx Mumba
  22. M

    Linear Algebra - Representing Matrix

    But this is what i wanted to do ^^. But i dont know how. I ve never seen this before... Thats why i asked is that Polynomial correct the way i have written it down? Maybe you can give me an example, lets say for 1+x... What should i do with this? Sorry but i really dont know...:(
  23. M

    Linear Algebra - Change of Bases

    Hi, again another problem: Let B1 = {( \stackrel{1}{3}),( \stackrel{1}{2})} and B_{2} = [ \frac{1}{\sqrt{2}}( \stackrel{1}{1}), \frac{1}{\sqrt{2}} (\stackrel{-1}{1}) ] Determine the representing matrix T = K_{B_{2},B_{1}} \in \Re^{2\times2} for the change from B1 coordinates to...
  24. M

    Linear Algebra - Representing Matrix

    yes, we called it R. sorry i meant the same. A transformations from <=2 to <=3....
  25. M

    Linear Algebra - Representing Matrix

    Homework Statement The Question: The map is given: L\rightarrow \Re_{2} \rightarrow \Re_{3}, p \rightarrow p' + q*p , with q(x) = x. Now i should find the representing matrix for L with respect to the bases {1+x, x+x2, 1+x2} for \Re_{2} and {1,x,x+x2,1+x3} for \Re_{3}. The Attempt...
  26. M

    Motion of charged particle in magnitc field given by potential of magnetic dipole

    Hi Thanks for the answer. But i cant go very far without a coordinate system, can I? I mean, using cyl. coordinates, my degrees of freedom would be just R and \Theta. So i can get the components of r=(Rcos\Theta, Rsin\Theta, z), where the z-axis is pointing upwards and \Theta the angle...
  27. M

    Motion of charged particle in magnitc field given by potential of magnetic dipole

    Find the fi rst integrals of motion for a particle of mass m and charge q in a magnetic field given by the vector potential (scalar potential \Phi= 0) (i) of a constant magnetic dipole m_{d} A=\frac{\mu_{0}}{4 pi}\frac{m_{d} \times r}{r^{3}} Hint: Cylindrical coordinates are useful...
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