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Registered Member #75
Joined: Thu Feb 09 2006, 09:30AM
Location: Montana, USA
Posts: 711
Here you go: plug in A and s into the first equation |sI-A|=0 and do the subtraction to get
det ( s-3 4
-2 s+1) = 0
now you follow the usual procedure to evaulate it:
(s-3)(s+1)+2*4 = 0
which simplifies to the result. HTH. If any of this is unclear, please let me know which part troubles you. It is kind of hard to go through this in detail with just ASCII
Registered Member #30
Joined: Fri Feb 03 2006, 10:52AM
Location: Glasgow, Scotland
Posts: 6706
If I remember right, "s" is the wee magic number you use when finding the eigenvalues of a matrix, and |sI-A|=0 is the equation you need to solve to find the eigenvalues of A. You have to use algebra to find the value of "s" that makes the equation true. Or values: there are usually several.
Once you know these values of "s" you can do something else (that I can't remember) to find an eigenvector for each one. Eigenvalues and eigenvectors are important in control engineering, the reason being that if the matrix A describes the dynamics of a system, then each solution to the above equation corresponds to a resonant mode of the system, and the eigenvectors tell you which parts will throb how hard and in which directions.
For instance, if you write the circuit equations for a DRSSTC and solve them using this method, you should find two solutions to the equation.
Registered Member #176
Joined: Tue Feb 14 2006, 09:35PM
Location:
Posts: 44
Steve Conner wrote ...
If I remember right, "s" is the wee magic number you use when finding the eigenvalues of a matrix, and |sI-A|=0 is the equation you need to solve to find the eigenvalues of A. You have to use algebra to find the value of "s" that makes the equation true. Or values: there are usually several.
Once you know these values of "s" you can do something else (that I can't remember) to find an eigenvector for each one. Eigenvalues and eigenvectors are important in control engineering, the reason being that if the matrix A describes the dynamics of a system, then each solution to the above equation corresponds to a resonant mode of the system, and the eigenvectors tell you which parts will throb how hard and in which directions.
For instance, if you write the circuit equations for a DRSSTC and solve them using this method, you should find two solutions to the equation.
Hi Steve,
Yes matrix algerba is inportant in control systems and this is what I am studying at the moment.
I handed the paper in tuesday after solving for S and solving the equations etc but my leacture said he would just be happy with:
Write the matrix in the form:
A B
C D
The determinant is calculated with the formula:
(ad) – (bc)
Adding information into the formula:
((s-3)* 2) – ((-4)*(s+1)) = 0
Simplifying the formula:
((s-3)* 2) – ((-4)*(s+1)) = 0
Multiplying out the brackets:
(S2 * -2S) + 5 = 0
This proves that the determinate = 0.
S is a Eignevalue in control engineering and thats where my confusion was. After chatting to him he realised that he should of changed the letter as the text books we follow discuss eigenvalues and S is defined as a constant when working out eignevalues.
I was expecting to have to solve a larger solution but he just wanted a proof of algerba techniques and using determinants.
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Maths Problem: Matrices
