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

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RAJA KUMAR 2023-11-8

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https://ww2.mathworks.cn/matlabcentral/answers/2044592-equivalent-impedance-using-matrix-eigen-value-and-eigen-vector-norm

编辑： RAJA KUMAR 2023-11-13

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I am solving this below problem(attachment 1). How to find the exp(theta1) and exp(theta2)...?

Attachment pdf.pdf is the problem I am trying to solve.
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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RAJA KUMAR 2023-11-9

I want all of my eigen values to be nonnegative

Walter Roberson 2023-11-9

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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