My Math Forum  

Go Back   My Math Forum > College Math Forum > Linear Algebra

Linear Algebra Linear Algebra Math Forum


Thanks Tree2Thanks
  • 2 Post By Greens
Reply
 
LinkBack Thread Tools Display Modes
April 14th, 2019, 01:11 PM   #1
Newbie
 
Joined: Apr 2019
From: turkey

Posts: 3
Thanks: 0

eigenvalues and eigenvectors

Hi,
I have a problem ,
Give an example to the T ϵ L(R ^ 4) operator with no real eigenvalues. Please explain
matamat19 is offline  
 
April 15th, 2019, 01:00 PM   #2
Global Moderator
 
Joined: May 2007

Posts: 6,732
Thanks: 689

Quote:
T ϵ L(R ^ 4)
Translate!
mathman is offline  
April 15th, 2019, 01:16 PM   #3
Senior Member
 
romsek's Avatar
 
Joined: Sep 2015
From: USA

Posts: 2,408
Thanks: 1310

Quote:
Originally Posted by mathman View Post
Translate!
$T$ is a linear transformation $\mathbb{R}^4 \to \mathbb{R}^4$
romsek is offline  
April 15th, 2019, 02:50 PM   #4
Newbie
 
Greens's Avatar
 
Joined: Oct 2018
From: USA

Posts: 19
Thanks: 13

Math Focus: Algebraic Geometry
So, where $\lambda$ is the eigenvalue, and $A$ is the transform matrix:

$\displaystyle AX=\lambda IX$

$\displaystyle (A-\lambda I)X = 0$

Since X can only be 0, we know that $(A-\lambda I)$ must be rank 4 and therefore $(A-\lambda I)$ is row equivalent to $I$. Therefore you need $A$ to be some matrix that stays rank 4 no matter what you add/subtract from the diagonals.

$A= \begin{bmatrix}
0 & 1 & 0 & 0 \\
0 & 0 & 2 & 0 \\
0 & 0 & 0 & 3 \\
4 & 0 & 0 & 0
\end{bmatrix} $

Works since no matter what lambda is the matrix won't have any empty rows or columns. In this case $T = AX$

EDIT: Made a mistake in the original, if there are only $1$'s vectors with all equal elements will be eigenvectors. Apologies
Thanks from topsquark and matamat19

Last edited by Greens; April 15th, 2019 at 03:20 PM. Reason: typos. Mistake Fixed
Greens is offline  
April 15th, 2019, 03:00 PM   #5
Newbie
 
Joined: Apr 2019
From: turkey

Posts: 3
Thanks: 0

thank you so much
matamat19 is offline  
April 15th, 2019, 03:51 PM   #6
Newbie
 
Joined: Apr 2019
From: turkey

Posts: 3
Thanks: 0

I have one more question...
Find the T is a linear transformation C3→C3 operator with eigenvalues 6 and 7 so that no matrix is diagonal
matamat19 is offline  
Reply

  My Math Forum > College Math Forum > Linear Algebra

Tags
eigenvalues, eigenvectors



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
What is Eigenvalues, Eigenvectors? integration Elementary Math 1 March 27th, 2018 04:20 AM
Eigenvalues + Eigenvectors calypso Linear Algebra 4 June 21st, 2016 08:46 AM
Eigenvalues and Eigenvectors hk4491 Linear Algebra 3 March 4th, 2014 01:03 PM
Help with eigenvalues and eigenvectors :) bonildo Linear Algebra 7 June 11th, 2012 04:06 PM
Eigenvalues and Eigenvectors bonildo Linear Algebra 4 June 8th, 2012 07:02 PM





Copyright © 2019 My Math Forum. All rights reserved.