How to determine eigenvalues and eigenvectors?

Question

Md Ashikuzzaman 2022-7-13

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1758585-how-to-determine-eigenvalues-and-eigenvectors

编辑： Abderrahim. B 2022-7-13

I have two matrices for example A and B. A=[3,9;3,5] and B=[2,0;0,8].

They are part of an eigenvalue problem of the form: (A-(lambda)B)x=0.

How do I find the eigenvalues and vectors using matlab? Please solve this problem using values and sharee the code from your monitor if possible.

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Answer 1

Bruno Luong 2022-7-13

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https://ww2.mathworks.cn/matlabcentral/answers/1758585-how-to-determine-eigenvalues-and-eigenvectors#answer_1005885

编辑：Bruno Luong 2022-7-13

在 MATLAB Online 中打开

A=[3,9;3,5]
A = 2×2
     3     9
     3     5
B=[2,0;0,8]
B = 2×2
     2     0
     0     8
[V lambda] = eig(A,B,'vector')
V = 2×2
    1.0000   -1.0000
    0.2074    0.4018
lambda = 2×1
    2.4332
   -0.3082
% here is the first eigen vector with lambda(1) the corresponfing eigen
% value
x1 = V(:,1)
x1 = 2×1
    1.0000
    0.2074
(A - lambda(1)*B)*x1 % small but not 0 due to finite precision floating point
ans = 2×1
1.0e-15 *

    0.2220
   -0.4441
% second eigen vector and second eigen value lambda(2)
x2 = V(:,2)
x2 = 2×1
   -1.0000
    0.4018
(A - lambda(2)*B)*x2 % small but not 0 due to finite precision floating point
ans = 2×1
1.0e-15 *

    0.8882
    0.4441

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Answer 2

Abderrahim. B 2022-7-13

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https://ww2.mathworks.cn/matlabcentral/answers/1758585-how-to-determine-eigenvalues-and-eigenvectors#answer_1005865

编辑：Abderrahim. B 2022-7-13

在 MATLAB Online 中打开

Use eig

A = [3,9;3,5];
[eVecs, eVals] = eig(A) 
eVecs = 2×2
   -0.9026   -0.8196
    0.4304   -0.5729
eVals = 2×2
   -1.2915         0
         0    9.2915

Eigenvalues are the diagonal elements of eVals. To get them use diag

eValues = diag(eVals)
eValues = 2×1
   -1.2915
    9.2915

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Answer 3

Chunru 2022-7-13

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https://ww2.mathworks.cn/matlabcentral/answers/1758585-how-to-determine-eigenvalues-and-eigenvectors#answer_1005870

在 MATLAB Online 中打开

% doc eig for more details
A=[3,9;3,5] 
A = 2×2
     3     9
     3     5
B=[2,0;0,8]
B = 2×2
     2     0
     0     8
[vA, dA] = eig(A)
vA = 2×2
   -0.9026   -0.8196
    0.4304   -0.5729
dA = 2×2
   -1.2915         0
         0    9.2915
[vB, dB] = eig(B)
vB = 2×2
     1     0
     0     1
dB = 2×2
     2     0
     0     8