why do I get different EigenVectors than my instructor got?

2020 10 5
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Steven Lord
Steven Lord 2020-10-5
编辑：Steven Lord 2020-10-5

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If v is an eigenvector of A corresponding to eigenvalue d, multiplying v by a non-zero scalar k results in another eigenvector of A with the same eigenvalue. In this case, the first column of V matches the eigenvector [2; 1] and the second matches [10; 7].
>> A = [0.6 0.5; -0.175 1.2];
>> [V, D] = eig(A);
>> k1 = 1./max(V(:, 1))
k1 =
-2.23606797749979
>> k1*V(:, 1)
ans =
2
1
>> k2 = 10./V(1, 2)
k2 =
-12.2065556157337
>> k2*V(:, 2)
ans =
10
7

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zolteckx6
zolteckx6 2020-10-5
% I really appreciate your time on this one!
A = [1 2 ; 5 4]
[V, D] = eig(A)
k1 = 1./max(V(:, 1))
k1*V(:, 1)
k2 = 10./V(1, 2)
W = k2*V(:, 2)
V2 = W/5
% a question of understanding
% doing the problem by hand naturally leads to V1 = [-1 1]
% and V2 = [2 5]
% plugging in -6 for labda gives (-5 2 ; 5 -2)
% I understand that [-985/1393 985/1393] = [-1 1]
% but why does matlab give me these values?

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