MHB Eigenvector Calculations and Verification for y1+y2=5

  • Thread starter Thread starter ertagon2
  • Start date Start date
  • Tags Tags
    Eigenvector
ertagon2
Messages
36
Reaction score
0
Can you please confirm my answer?
View attachment 7539
det(yI-A) = 0
(y-1)(y-4)=0
y1+y2=5
 

Attachments

  • 2.png
    2.png
    2.3 KB · Views: 122
Physics news on Phys.org
Yes, it is correct.

Incidentally, did you already learn about the eigenvalues of triangular matrices?
Did you perhaps already learn about the trace of a matrix (= the sum along the main diagonal)?

This could help you to calculate the required quantity without having to set up the characteristic polynomial. (Of course, that is not much work here, either.)
 
I get the characteristic equation:

$$x^2-(1+4)x+(1\cdot4-0\cdot3)=x^2-5x+4=(x-1)(x-4)=0$$

Hence:

$$\lambda_1+\lambda_2=1+4=5\quad\checkmark$$

W|A confirms our results:

W|A - eigenvalues for ((1,0),(3,4))
 

Thread 'Trouble understanding an online solution to an exercise in Dummit & Foote'

##\textbf{Exercise 10}:## I came across the following solution online: Questions: 1. When the author states in "that ring (not sure if he is referring to ##R## or ##R/\mathfrak{p}##, but I am guessing the later) ##x_n x_{n+1}=0## for all odd $n$ and ##x_{n+1}## is invertible, so that ##x_n=0##" 2. How does ##x_nx_{n+1}=0## implies that ##x_{n+1}## is invertible and ##x_n=0##. I mean if the quotient ring ##R/\mathfrak{p}## is an integral domain, and ##x_{n+1}## is invertible then...
View full post »

Thread 'Questions about non existence of GCDs vs (coimages, cokernels)'

The following are taken from the two sources, 1) from this online page and the book An Introduction to Module Theory by: Ibrahim Assem, Flavio U. Coelho. In the Abelian Categories chapter in the module theory text on page 157, right after presenting IV.2.21 Definition, the authors states "Image and coimage may or may not exist, but if they do, then they are unique up to isomorphism (because so are kernels and cokernels). Also in the reference url page above, the authors present two...
View full post »

Thread 'Decomposition into irreps of compact Lie group'

When decomposing a representation ##\rho## of a finite group ##G## into irreducible representations, we can find the number of times the representation contains a particular irrep ##\rho_0## through the character inner product $$ \langle \chi, \chi_0\rangle = \frac{1}{|G|} \sum_{g\in G} \chi(g) \chi_0(g)^*$$ where ##\chi## and ##\chi_0## are the characters of ##\rho## and ##\rho_0##, respectively. Since all group elements in the same conjugacy class have the same characters, this may be...
View full post »

Similar threads

MATLAB Averaging two data with different domains
Replies
4
Views
1K
Taps for simple IIR Filter in GNU Radio
Replies
1
Views
2K
MHB 3.2.5.3 General Solution if system
Replies
14
Views
2K
Understanding Cardano's method of solving Cubic equation
Replies
3
Views
3K
Using ODE45 on Matlab to Integrate A Problem
Replies
1
Views
2K
Eigenvalue problem -- Elastic deformation of a membrane
Replies
9
Views
5K
MHB How can I calculate the union of two rotated rectangles using an algorithm?
Replies
8
Views
5K
I Eigenvectors for degenerate eigenvalues
Replies
7
Views
9K
Comp Sci Linear regression doubling time
Replies
2
Views
1K
Deconvolution of fluorescence spectra
Replies
1
Views
3K

Hot Threads

Recent Insights

Back
Top