Equivalent Impedance using Matrix, Eigen value and Eigen vector, norm

2023 11 8
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更新时间：2023 11 13
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I am solving this below problem(attachment 1). How to find the exp(theta1) and exp(theta2)...?
  1. Attachment pdf.pdf is the problem I am trying to solve.
  2. Attachment Tzeng_2006_J._Phys._A__Math._Gen._39_8579.pdf is the theory
Y11 =1-1i/sqrt(3); Y12 =1i/sqrt(3); Y13 =-1;
Y21 =1i/sqrt(3); Y22 =0; Y23 =-1i/sqrt(3);
Y31 =-1; Y32 =-1i/sqrt(3); Y33 =1+1i/sqrt(3);
Y11 = Y12 + Y13 ; Y22 = Y21 + Y23 ; Y33 = Y31 + Y32 ;
L = [Y11, Y12, Y13; Y21, Y22, Y23; Y31, Y32, Y33];
[EVector,EValue] = eig(L'*L) ; % V = Values % D = VECTORS
Sigma_2 = sqrt(EValue(2,2))
Sigma_3 = sqrt(EValue(3,3))

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John D'Errico
John D'Errico 2023-11-8
You already know how to use eig. It returns all of the eigenvalues, and their associated eigenvectors.
Throw away all of the eigenvalues that are negative, as well as the eigenvectors associated with the ones you don't want. Toss any that are complex too, if that is a problem. What remains are the non-negative eigenvalues, as well as their eigenvectors.
So where is the problem?
RAJA KUMAR
RAJA KUMAR 2023-11-9
I want all of my eigen values to be nonnegative
Walter Roberson
Walter Roberson 2023-11-9
Ran in:
Ran in:
Q = @(v) sym(v);
Y11 = 1-1i/sqrt(Q(3)); Y12 = 1i/sqrt(Q(3)); Y13 = Q(-1);
Y21 = 1i/sqrt(Q(3)); Y22 = Q(0); Y23 = -1i/sqrt(Q(3));
Y31 = -1; Y32 = -1i/sqrt(Q(3)); Y33 = 1+1i/sqrt(Q(3));
Y = [Y11, Y12, Y13; Y21, Y22, Y23; Y31, Y32, Y33; Y41, Y42, Y43]
Unrecognized function or variable 'Y41'.
A = L'*L ; % e = eig(L_P*L);
[V,EVC] = eig(A) % V = Values % D = VECTOR

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RAJA KUMAR
RAJA KUMAR
2023-11-8

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RAJA KUMAR
RAJA KUMAR
2023-11-13

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