Which Right Eigenvector to report?

1 view (last 30 days)
AHMAD KHUSYAIRI CHE RUSLI on 23 Dec 2019
Commented: Ridwan Alam on 30 Jan 2020
%%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
>>

Ridwan Alam on 23 Dec 2019
Edited: Ridwan Alam on 30 Jan 2020
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 on 30 Jan 2020
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 on 30 Jan 2020
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.

Christine Tobler on 6 Jan 2020
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).

1 Comment

AHMAD KHUSYAIRI CHE RUSLI on 30 Jan 2020