Triple eigenvalue with 3 linearly independent eigenvectors, Programming Languages

Assignment Help:

1 Triple Eigenvalue with 3 Linearly Independent Eigenvectors

In this case we will have the eigenvalue l with the three linearly independent eigenvectors  ?h1, ?h2 and  ?h3  thus we find the following three linearly independent solutions,

elt  ?h1                         elt  ?h2                         elt  ?h3

4 x 4 Systems

We will close this section out along with a couple of comments about 4x4 systems. In these cases we'll contain 4 eigenvalues and will require 4 linearly independent solutions in order to find a general solution. The vast majorities of the cases this time are natural extensions of what 3x3 systems cases and actually will use a vast majority of that work.

Now there are a couple of new cases which we must comment briefly on though. With 4x4 systems this will now be possible to contain two different sets of double eigen-values and two dissimilar sets of complex conjugate eigen-values. In either of these cases we can use each one as a separate case and utilize our previous knowledge regarding to double eigenvalues and complex eigenvalues to find the solutions we require.

This is also now possible to contain a "double" complex eigenvalue. Conversely we can have l = (a + bi) each occurs double in the list of eigenvalues. The solutions for that case aren't too bad.  We find two solutions in the normal method of dealing along with complex eigenvalues. The rest two solutions will approach from the work we did for a double eigenvalue. The work we did there which case did not need such the eigenvalue/vector pair to be real. Thus if the eigenvector related withl = (a + bi) is   then the second solutiuon will be as,

 t e(a + bi) t ?h + e(a + bi )t ?r         here  ?r satisfies (A -lI)  ?r =  ?h

And once we've determined ?r  we can again split it up in its real and imaginary parts by using Euler's formula to find two new real valued solutions.

 At last with 4 x 4 systems we can now contain eigenvalues with multiplicity of 4. In these cases we can contain 1, 2, 3, or 4 linearly independent eigenvectors and we can utilize our work along with 3x3 systems to notice how to generate solutions for such cases. The one matter which you'll require to pay attention to is the conditions for the 2 and 3 eigenvector cases will have identical complications as the 2 eigenvector cases has in the 3 x 3 systems.

Therefore, we've discussed several of the matters involved in systems larger than 2 x 2 and this is hopefully clear that while we move into larger systems the work can be turn into vastly more complex.

Related Discussions:- Triple eigenvalue with 3 linearly independent eigenvectors

Program for nuclear reactor - embedded systems, Implement the "Nuclear Reac...

Implement the "Nuclear Reactor" example using the following:  An ISR triggered by a button press  A task to update the temperatures  A semaphore to communicate between the ISR and

Write a program that draws the initials j, Write a program that draws the i...

Write a program that draws the initials J G P on the form similar to that shown in Fig J 1 (using straight lines and curve semicircles). The figure can not have corners. All ends a

Define remote procedure call, Problem: (i) Define Remote Procedure Cal...

Problem: (i) Define Remote Procedure Call (RPC). (ii) Explain with diagram how RPC works? (iii) A remote procedure is uniquely defined by (a) Program number. (b)

Jsp project, Eclipse Jsp Project. I am making a a project on my website and...

Eclipse Jsp Project. I am making a a project on my website and i was making a help support page on which the user can submit their question and the question is saved to a text file

Write a constructor for money data structure, Create a Money data structure...

Create a Money data structure that is made up of amount and currency.  (a) Write a constructor for this data structure   (b)  Create accessors for this data structure (c)

Java, non restoring division

non restoring division

Create a clickable map - web operating system, You are required to develop ...

You are required to develop a content management system for the following scenario:   "A Travel Information (NTIK) system is to be designed to allow travellers to access to an elec

Undetermined coefficients, We now require starting looking into finding a p...

We now require starting looking into finding a particular solution for n th order differential equations. The two ways which we'll be looking at are similar as those which we look

Pascal program, Pascal program: Exactly what you need to do to generat...

Pascal program: Exactly what you need to do to generate your empirical data is specific to your individual assignment. However, some rules apply to all of you: 1. The gener

Write Your Message!

Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd