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Solving equations for Eigenvector: Vanishing

  • Thread starter zak100
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  • #1
zak100
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Homework Statement


I am trying to solve a Eigen vector matrix:

##\begin{bmatrix}9.2196& 6.488\\4.233& 2.9787\end{bmatrix}\cdot\begin{bmatrix}x\\y\end{bmatrix}-\lambda\begin{bmatrix}x\\y \end{bmatrix}=0##

I have found ##\lambda_1 = 0## and ##\lambda_2 = 12.1983##
However, I cant solve the following equations:
##9.2196x + 6.488y =0 -------(eq.1)##
and ##4.233x + 2.978y =0 ----(eq.2)##

I am multiplying ##(eq.1) ## by ##4.233x## and ##(eq.2)## by ##9.2196##

Some body please guide me how to solve these equations for ##x## and ##y## values.

Zulfi.

Homework Equations


##9.2196x + 6.488y =0 -------(eq.1)##
and ##4.233x + 2.978y =0 ----(eq.2)##

The Attempt at a Solution


I am multiplying ##(eq.1)## by ##4.233## and ##(eq.2)## by ##9.2196## but both the equations are vanishing. Some body please guide me.

Zulfi.
 

Answers and Replies

  • #2
PeroK
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Homework Statement


I am trying to solve a Eigen vector matrix:

##\begin{bmatrix}9.2196& 6.488\\4.233& 2.9787\end{bmatrix}\cdot\begin{bmatrix}x\\y\end{bmatrix}-\lambda\begin{bmatrix}x\\y \end{bmatrix}=0##

I have found ##\lambda_1 = 0## and ##\lambda_2 = 12.1983##
However, I cant solve the following equations:
##9.2196x + 6.488y =0 -------(eq.1)##
and ##4.233x + 2.978y =0 ----(eq.2)##

I am multiplying ##(eq.1) ## by ##4.233x## and ##(eq.2)## by ##9.2196##

Some body please guide me how to solve these equations for ##x## and ##y## values.

Zulfi.

Homework Equations


##9.2196x + 6.488y =0 -------(eq.1)##
and ##4.233x + 2.978y =0 ----(eq.2)##

The Attempt at a Solution


I am multiplying ##(eq.1)## by ##4.233## and ##(eq.2)## by ##9.2196## but both the equations are vanishing. Some body please guide me.

Zulfi.
The two equations are equivalent. So, you just take the solution of either one.
 
  • #3
hilbert2
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And, it only determines the solution up to a constant multiplier, so you can for example arbitrarily set ##x=1## and then find ##y##.
 
  • #4
zak100
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Hi,
Thanks for your response. Answer is different in the slide. I have attached the slide. Please guide me.

Solving Decimal eq for Eigen vectors LDA vanishing_PicOfSlide.jpg
 

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  • #5
hilbert2
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In the solution for ##w_1##, the ratio of the components ##\frac{0.8178}{0.5755}## is the same as the ratio ##\frac{9.2196}{6.488}## in your system of equations. So it's the same answer but with different normalization, one where ##x^2 + y^2 = 1##.
 
  • #6
zak100
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Hi,
##lambda_2 =12.1983##
I am not able to get the correct answer.

##9.2196x + 6.488y = 12.1983x ##
##9.216x - 12.1983x = -6.488y ##

##\begin{bmatrix}x\\y\end {bmatrix} = \begin{bmatrix}2.7\\1\end{bmatrix}##

Somebody please guide me how can i get the correct answer?
Zulfi.
 

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