@Carl Love Thank you so much! I new there was a simple solution, I was just having trouble finding documentation on it

@Carl Love Additionally, I am trying to replace the eigenvalues (corresponding to velocity propogation) of my system with the variable lambda but it doesnt seem to replace all of the values and there isnt the denominator issue. Any insight is greatly appreciated. Thanks! Generalized_3D_Eigensystem.mw

@Carl Love Thats intersting that you say that because my solution changes between two or three different solutions (one being significantly shorter than the others). This is probably the solution you were working with. I am assuming that all the solutions are algebraically identical but something strange is going on with the simplify command that changes it each time I run the code. Any idea as to what is causing this? Thanks for the help!

@Joe Riel Here is my attempt with your method. Did I input this in incorrectly?Generalized_3D_Eigensystem.mw

Attached is my attempt with using the subs command (I had tried this previously). This ultimatley did not work. Am I doing something wrong?Generalized_3D_Eigensystem.mw

Apologies, here is the fileGeneralized_3D_Eigensystem.mw

@acer I am working with a computational fluid dynamics solver which is currently a 2 dimensional solver (in Fortran). My goal is to expand this solver to three dimensions. The 2D solver was written in such a way that the computation talked about in this thread was done analytically. To avoid scrapping this entire portion of the code (and avoid changing other subroutines), I was hoping to do an analytic computation in 3D such that it could easily be implemented in Fortran. As we have seen, analytical solutions to this problem are too complex, and I will more than likely need to rely on numerical computations. I have some ideas on how this solution could possibly be obtained analytically (possibly with some clever substitution or rewriting my independed variables in non-conservative form). More than likely, this will fail and I will need to rewrite a large portion of the code in order to implement something such as LAPACK. I will continue to try more analytical methods first, however. Thank you very much for your help over the past couple of days as I am not used to using MAPLE, your help is very appreciated. 

@acer Please Ignore my previous post, I got my variables mixed up. Thank you for youre help, I agree that they are the same.

@acer So the variables printed out at the end of my origional file (evecsA and A) are both ocrrect? Im just a little confused because the top row of the variable A has zeros while evecA does not. This is just due to a linear combination?

1D_Euler_Eigenvectors.mw @acer I apologize for coming back to this post, but I beleive there are some discrepencies between the instrinic function eigenvectors and the code that you wrote in the file you uploaded (eigs.mw). The problem I was origionally working on was a 3D fluid problem so I am attempting to solve it in 1D to make the computations much easier in an attempt to see where I am going wrong. With that said, the file that I uploaded calculates the eigenvector of the 1 dimensional problem using two methods, the intrinsic eigenvector function and the code that you wrote. As you can see, these solutions are not the same. I was wondering if you had an answer to why this is the case? Thank you for your help once again. 

@acer @dharr478 I apologize for my trouble communicating. The truth is I dont think I am understanding and matching the math to the physics correctly. I think I need to read up on my linear algebra before attempting to tackle this problem again. Thank you very much for your help, I know have a tool to compute the eigenvectors when I get to that point. I am really appreciative of your help.

@acer Furthermore, the constraint c and rho are greater than zero can also be assumed. I am not sure if this could change things. As I said I am new to Maple so I dont know if I can program that correctly

@acer The eigenvalues are exactly what I expected. In fact, I know that the eigenvalues are correct. What I expected was for each Eigenvalue to have only one eigen vector associated with it. Since the last four eigenvalues are identical, they should have the same eigenvector(s) as mentioned earlier. What I did not expect is for each eigenvalue to have four eigenvectors associated with it. What i expected was to have six total eigenvectors (one eigenvector for each eigenvalue). Does this clear things up? Sorry for the confusion

@acer Thank you all for your help and suggestions. I need to brush up on my linear algebra a little bit but with that said, the physical problem I am trying to solve is for computational fluid dynamics. What I expected the solution to look like (as other similar solutions look like) is for each eigenvalue to have only one eigenvector associated with it. With this, I could theoretically construct a matrix of eigenvectors (6X6 for this case since I have 6 eigenvalues) and continue my math from there. Because there are four eigenvectors corresponding to each eigenvalue, I am stuck an unable to continue my math. Long story short, the correct physical solution should have one eigenvector for each eigenvalue theoretically. The problem is that my matrix A should be correct because I know what the eigenvalues should be (and the ones computed are correct) so I am confused with the solution. 

@acer Wow, thank you so much for the amazing help. I really appreciate that. So all of my eigenvectors are zeros?