Eigenvectors, does order matter?

In summary, eigenvectors can be any scalar multiple of the original vector and the order of the components in the vector does not matter.
  • #1
charlies1902
162
0
I got 2 questions about eigenvectors.

Let's say you have an eigenvector [1 0 2]^t.


1. Does the order matter? Like can I change the order to [0 1 2]^t or [1 2 0]^t?


2. It can be any scalar multiple of the vector right? Like I could have [2 0 4] or [4 0 8]
 
Physics news on Phys.org
  • #2
charlies1902 said:
I got 2 questions about eigenvectors.

Let's say you have an eigenvector [1 0 2]^t.


1. Does the order matter? Like can I change the order to [0 1 2]^t or [1 2 0]^t?


2. It can be any scalar multiple of the vector right? Like I could have [2 0 4] or [4 0 8]

Scalar multiples are still eigenvectors, sure. Show me why. Does order of the components in the vector matter? What would make you think it doesn't??
 
  • #3
The vector <1, 0, 0> is NOT the same as the vector <0, 1, 0> which appears to be what you are asking!
 

FAQ: Eigenvectors, does order matter?

What are Eigenvectors?

Eigenvectors are special vectors that represent the direction of a linear transformation without changing its direction. They are often used in the field of linear algebra to analyze and solve complex systems of equations.

How are Eigenvectors calculated?

Eigenvectors are calculated by finding the non-zero solutions to the equation A*v = λ*v, where A is a square matrix, v is the eigenvector, and λ is the corresponding eigenvalue. This can be done through various methods such as the power method or the QR algorithm.

What is the significance of Eigenvectors?

Eigenvectors are significant because they provide a way to understand and analyze complex systems of equations. They also have various applications in fields such as physics, engineering, and computer science.

Does the order of Eigenvectors matter?

Yes, the order of Eigenvectors does matter. The corresponding eigenvalues and eigenvectors must be in the same order to correctly represent the linear transformation. Changing the order can result in incorrect calculations and interpretations.

Can Eigenvectors be used for any matrix?

No, Eigenvectors can only be calculated for square matrices. The dimensions of the matrix must be n x n in order to find n eigenvectors and their corresponding eigenvalues.

Similar threads

Prove 9 is eigenvalue of ##T^2\iff## 3 or -3 eigenvalue of ##T##.
Replies
5
Views
1K
Find Matrix P and the Diagonal Matrix D
Replies
2
Views
746
Question regarding eigenvectors
Replies
7
Views
2K
Linear homogenous system with repeated eigenvalues
Replies
2
Views
1K
How do I know if my eigenvectors are right?
Replies
12
Views
2K
Fundamental matrix for complex linear DE system
Replies
4
Views
842
Solving a system of differential equations by fundamental matrix
Replies
8
Views
2K
Find the eigenvalues and eigenvectors
Replies
6
Views
2K
Normalisation of eigenvectors convention for exponentiating matrices
Replies
20
Views
2K
How to draw phase portrait for 2x2 nonlinear system of DE?
Replies
1
Views
843

Hot Threads

Recent Insights

Back
Top