Find the set of eigenvectors of a 4x4 matrix elements whose matrix elements have some VARIABLE PARAMETERS.
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Below is how I defined the matrix. It is a 4x4 matrix with variables B and N on the off diagonal. Since each of these variable takes certain values in a given range, my goal is to read and display the eigenvectors for each of the values in the range of the variables.
delta=45;
%create a 4x4 zeros matrix
mat=zeros(4,4);
%set values for corresponding entries of the matrix
mat(1,1)= delta;
mat(1,2)= 0 ;
mat(1,3)=0;
mat(2,1)=0 ;
mat(2,2)= delta;
mat(2,4)=0;
mat(3,1)=0;
mat(3,3)= -delta;
mat(3,4)= 0 ;
mat(4,2)=0;
mat(4,3)=0 ;
mat(4,4)= -delta;
%define the off diagonal elements of the matrix
for N = 0:1:5
for B = 0:0.001:10
mat(1,4)=sqrt(750*B*N);
mat(2,3)=sqrt(750*B*N);
mat(3,2)=sqrt(750*B*N);
mat(4,1)=sqrt(750*B*N);
end
end
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回答(3 个)
Jon
2022-11-11
If I understand what you are trying to do I think this should do what you want.
The resulting values of the eigenvector for each value of the parameter B*N will be stored in the columns of matrix V
delta=45;
%set values for corresponding diagonal entries of the matrix
mat = diag([delta,delta,-delta,-delta]);
% define vectors of variable parameters
N = 0:1:5;
B = 0:0.001:10;
% matrix is parameterized by product B*N, so just compute for unique
% values of this parameter
BN = unique(N'*B);
%define the off diagonal elements of the matrix and compute the
%eigenvectors
numParam = numel(BN); % number of parameter values to be evaluated
V = zeros(4,numParam); % preallocate array to hold eigenvectors
for k = 1:numParam
a = sqrt(750*BN(k));
mat(1,4)=a;
mat(2,3)=a;
mat(3,2)=a;
mat(4,1)=a;
V(:,k) = eig(mat);
end
3 个评论
Jon
2022-11-11
编辑:Jon
2022-11-11
Yes, good catch. The syntax seems a little strange with this, e = eig(A) returns a vector of eigen values, and so does [e] = eig(A), but [V,~]=eig(A) returns the matrix of eigenvectors. So even though in both cases we look at the first returned argument, the definition changes. So you must use the two argument calling syntax to get the eigenvectors.
This also means you need to store a matrix of Eigenvectors for each value of B*N, here is some modified code where I store the matrices of eigenvectors in a 3d array (each page is for a value of B*N).
So if you wanted look at the eigenvectors corresponding to BN(3) you would look at V(:,:,3)
delta=45;
%set values for corresponding diagonal entries of the matrix
mat = diag([delta,delta,-delta,-delta])
% define vectors of variable parameters
N = 0:1:5;
B = 0:0.001:10;
% matrix is parameterized by product B*N, so just compute for unique
% values of this parameter
BN = unique(N'*B);
%define the off diagonal elements of the matrix and compute the
%eigenvectors
numParam = numel(BN); % number of parameter values to be evaluated
V = zeros(4,4,numParam); % preallocate array to hold eigenvectors
for k = 1:numParam
a = sqrt(750*BN(k));
mat(1,4)=a;
mat(2,3)=a;
mat(3,2)=a;
mat(4,1)=a;
[V(:,:,k),~] = eig(mat);
end
Torsten
2022-11-11
编辑:Torsten
2022-11-12
I set a = sqrt(750*B*N) in the below code. So for every combination of B and N, it gives you the eigenvalues (diagonal of D) and eigenvectors (columns of V) of your matrix "mat".
syms delta a real
mat = delta*sym(eye(4));
mat(3,3) = -mat(3,3);
mat(4,4) = -mat(4,4);
mat(1,4) = a;
mat(4,1) = a;
mat(3,2) = a;
mat(2,3) = a;
[V,D] = eig(mat)
simplify(mat*V-V*D)
Walter Roberson
2022-11-11
I showed you in https://www.mathworks.com/matlabcentral/answers/1848378-how-to-read-the-eigenvectors-of-a-4x4-matrix-elements-for-a-given-range-of-variable-elements-b-and-n#answer_1096903 how to loop over the elements of B and record the values properly.
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