MATLAB Answers

Which Right Eigenvector to report?

15 views (last 30 days)
AHMAD KHUSYAIRI CHE RUSLI
AHMAD KHUSYAIRI CHE RUSLI on 23 Dec 2019
Commented: Ridwan Alam on 30 Jan 2020 at 15:33
%%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
>>

  0 Comments

Sign in to comment.

Answers (2)

Ridwan Alam
Ridwan Alam on 23 Dec 2019
Edited: Ridwan Alam on 30 Jan 2020 at 4:21
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.

  2 Comments

AHMAD KHUSYAIRI CHE RUSLI
AHMAD KHUSYAIRI CHE RUSLI on 30 Jan 2020 at 7:26
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
Ridwan Alam on 30 Jan 2020 at 15:33
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.

Sign in to comment.


Christine Tobler
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
AHMAD KHUSYAIRI CHE RUSLI on 30 Jan 2020 at 3:59
Thank you for the answer,
but I still not clear the value of right eigencertor to report.

Sign in to comment.

Sign in to answer this question.