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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

    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
  3. 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...
  4. 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...
  5. 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...