Linearly Independent Eigen Vectors

Click For Summary

Discussion Overview

The discussion revolves around the identification and calculation of eigenvalues and eigenvectors, specifically focusing on the linear independence of eigenvectors. It includes elements of homework-related inquiry and mathematical reasoning.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant initially claims to have found eigenvalues of 3 and -3, with corresponding eigenvectors of [1, 1] and [8, 2], but later acknowledges an error in their calculations.
  • Another participant requests to see the work behind the calculations rather than just the results.
  • A participant suggests that the matrix in question might be Hermitian, but notes that the book indicates a different answer.
  • A later post clarifies that the eigenvalues are actually both +3, leading to the conclusion that there is only one linearly independent eigenvector, which is [1, -1].
  • Some participants express agreement with the clarification regarding the eigenvectors.

Areas of Agreement / Disagreement

There is no consensus on the initial eigenvalues and eigenvectors, as participants initially present conflicting information. However, a later post clarifies that there is only one linearly independent eigenvector associated with the eigenvalue of +3, which some participants agree upon.

Contextual Notes

There are unresolved aspects regarding the interpretation of the matrix type (Hermitian) and the implications for eigenvalues and eigenvectors. The discussion also reflects uncertainty in the calculations presented by the participants.

jaus tail
Messages
613
Reaction score
48
Solved (sorry i tried again and realized my E-values were wrong)
1. Homework Statement
upload_2018-1-30_14-46-49.png


Homework Equations


Find Eigen Values and then what?

The Attempt at a Solution


I got eigen values as 3 and -3.
Now how to proceed?
I got Eigen Vector as: 1, 1 for eigen value of 3
and eigen vector as 8, 2 for eigen value of -3
so these are 2 independent eigen vector.
Book answer is B.
How?
 

Attachments

  • upload_2018-1-30_14-46-49.png
    upload_2018-1-30_14-46-49.png
    2.4 KB · Views: 755
Last edited:
Physics news on Phys.org
Show your work, not just the results, please
 
  • Like
Likes   Reactions: jaus tail
Okay. Will be careful for next time.
I'm struggling with this question. Thought of posting here instead of in other thread.
upload_2018-1-30_17-7-35.png

I think it's hermition matrix as A = (transpose and then conjugate of A)
But book says answer is D.
 

Attachments

  • upload_2018-1-30_17-7-35.png
    upload_2018-1-30_17-7-35.png
    3 KB · Views: 334
jaus tail said:
Thought of posting here instead of in other thread
Better to start a new thread: you get more help that way, too !

Post #1 resolved ?
 
  • Like
Likes   Reactions: jaus tail
Yes post#1 is solved. I had calculated wrong Eigen Values. Eigen values are +3, and +3. For +3 Eigen Vectors are [+1, -1] and there is no other combination of Eigen Vector that isn't a linear multiple of this vector. So there's only 1 Eigen Vector.
 
  • Like
Likes   Reactions: BvU
For post #3 I agree with you.
 
  • Like
Likes   Reactions: jaus tail
Thanks.
 

Similar threads

Calculating Eigenvectors: 3*3 w/o Augmented Matrix
  • · Replies 13 ·
Replies
13
Views
2K
How Can I Find Eigenvalues and Normalized Eigenvectors for a Matrix?
  • · Replies 2 ·
Replies
2
Views
2K
How to Calculate <Ly^2> Without Using Symmetry?
  • · Replies 6 ·
Replies
6
Views
2K
How Do You Find Eigenvectors of a 2x2 Matrix?
  • · Replies 6 ·
Replies
6
Views
2K
Show that eigenvalue of A + eigvalueof B ≠ eigvalue of A+B?
  • · Replies 28 ·
Replies
28
Views
6K
Graduate Eigenvector of Pauli Matrix (z-component of Pauli matrix)
  • · Replies 2 ·
Replies
2
Views
3K
Value of cos(x) where x is multiple of a matrix
  • · Replies 7 ·
Replies
7
Views
3K
How do I know if my eigenvectors are right?
  • · Replies 12 ·
Replies
12
Views
3K
Evaluating a wrong value of Eigenvector
  • · Replies 10 ·
Replies
10
Views
2K
Determinant of exponential matrix
  • · Replies 6 ·
Replies
6
Views
3K