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...
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)
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
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...
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
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...:(
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...
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...
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...
Find the first 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...