Eigen value and eigen vector of symbolic block matrix

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ASHA RANI 2021-5-18

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https://ww2.mathworks.cn/matlabcentral/answers/833398-eigen-value-and-eigen-vector-of-symbolic-block-matrix

评论： ASHA RANI 2021-5-19

clc
syms a51 a53 a54 a56 a62 a65 a67 a68 a71 a73 a74 a76 a81 a83 a84 a86 e
A= zeros(4);
B=eyes(4);
C=[a51 0 a53 a54; 0 a62 0 0;a71 0 a73 a74;a81 0 a83 a84];
F=[ 0 a56 0 0;a65 0 a67 a68;0 a76 0 0;0 a76 0 0];
G=[A;B;C;D]
[V,D]=eig(A)

I want to find all eigen values and eigen vectors of block matrix G. If I used code [V,D]=eig(A), its takes lot of times and not return any result.

if there any code to solve this type of matrix in less time. plz help

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ASHA RANI 2021-5-19

Yes, for this matrix the characteristic polynomial can be reduced to a fourth order equation with the eigenvalues being the positive and negative square roots of the roots of that equation.

But how this result help to find expresion for eigen value of G and also eigen vector?

plz help

Sulaymon Eshkabilov 2021-5-19

A = zero(4);

And you are trying to compute:

eig(A) that is equivalent of: eig(zero(4))

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回答（1 个）

Sulaymon Eshkabilov 2021-5-19

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THere are a few errs that need to be fixed before computing eigen values and vectors.

syms a51 a53 a54 a56 a62 a65 a67 a68 a71 a73 a74 a76 a81 a83 a84 a86 e
A= zeros(4);
B=eye(4);
C=[a51 0 a53 a54; 0 a62 0 0;a71 0 a73 a74;a81 0 a83 a84];
F=[ 0 a56 0 0;a65 0 a67 a68;0 a76 0 0;0 a76 0 0];
G=[A, B;C, F]
[V,D]=eig(G)
doc eig   % Get some good help from MATLAB documentation library.