Which Right Eigenvector to report?

%%Using the data below, what is right eigenvector for A? If V1 0.5662 0.2168 -0.8347, which one is right eigenvector? how about V2 and V3?

>> A=[0 -1 2 ; 5 0 4 ; 7 -2 0];

[V,D,W]=eig(A)

v1=V(1:end,1)

v2=V(1:end,2)

v3=V(1:end,3)

V =

0.5062 + 0.0000i -0.1323 - 0.2072i -0.1323 + 0.2072i

0.2168 + 0.0000i -0.8538 + 0.0000i -0.8538 + 0.0000i

-0.8347 + 0.0000i -0.2323 - 0.3959i -0.2323 + 0.3959i

D =

-3.7259 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i

0.0000 + 0.0000i 1.8630 + 3.0679i 0.0000 + 0.0000i

0.0000 + 0.0000i 0.0000 + 0.0000i 1.8630 - 3.0679i

W =

0.8860 + 0.0000i 0.7895 + 0.0000i 0.7895 + 0.0000i

-0.0111 + 0.0000i -0.2759 - 0.3553i -0.2759 + 0.3553i

-0.4636 + 0.0000i 0.4072 - 0.0923i 0.4072 + 0.0923i

v1 =

0.5062

0.2168

-0.8347

v2 =

-0.1323 - 0.2072i

-0.8538 + 0.0000i

-0.2323 - 0.3959i

v3 =

-0.1323 + 0.2072i

-0.8538 + 0.0000i

-0.2323 + 0.3959i

>>

Answer 1

[Ridwan Alam]

I assume you meant 'right' as opposed to 'left' eigen vectors.

[V,D] = eig(A); % to get left eigenvectors, [V,D,W] = eig(A), here W has the left eigen vectors
% right eigen vectors and eigen values
V1 = V(:,1); D1 = D(1,1);
V2 = V(:,2); D2 = D(2,2);
V3 = V(:,3); D3 = D(3,3);

V1, V2, and V3 are the right eigen vectors of A, as

A*V1 - V1*D1 % is very small, near zero
A*V2 - V2*D2 % is very small, near zero
A*V3 - V3*D3 % is very small, near zero

Hope this helps.

[AHMAD KHUSYAIRI CHE RUSLI]

Hi Ridwan Alam. Thanks for the answer. But, I little bit confuse when I discuss with my friend, is it D1 = -3.7259? So what is v1 =v(:,1)? Because Im looking for single value, for example right eigenvalue for V= 3.2 ,D=0.6, W= 2.1 or i failed to understand the concept?

[Ridwan Alam]

Hi Ahmad, the eigen value is a scalar "value", but the eigen vectors are "vectors".

Here, D1 is your eigen VALUE (scalar) for the corresponding eigen VECTOR V1.

Hope this makes sense.

For more details: https://en.wikipedia.org/wiki/Eigenvalues_and_eigenvectors

Answer 2

[Christine Tobler]

The left and right eigenvectors are matched one-by-one. For example, for [V, D, W] = eig(A), the eigenvalue D(k, k) corresponds to the right eigenvector V(:, k) and the left eigenvector W(:, k). In other words, A*V = V*D and A'*W = W*conj(D).

[AHMAD KHUSYAIRI CHE RUSLI]

Thank you for the answer,

but I still not clear the value of right eigencertor to report.