- #1
DaVinci
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I have a homework problem here I am a little at a loss on due to not very good examples in class and the part of the book that explains them is 4 chapters ahead and loaded with words I just do not understand yet. If someone could give a definition or two and get me started on this bad boy, I'd appreciate it.
The problem itself is:
Diagonalize the matrix A below. Normalize the eigenvectors so that they are unit vectors.
[TEX]
A = \left( {\begin{array}{*{20}c}
3 & {\sqrt 5 } \\
{\sqrt 5 } & { - 1} \\
\end{array}} \right)
[/TEX]
Code above is in work to look right... until then... remove the :
A = 3 : sgrt(5)
::sqrt(5) : -1
Now that the problem is stated, I will show my thoughts and what I am lacking in...
Diagonalizing the matric is basically taking A and getting A', where a'11, a'22, and a'33 (the diagonal) are the eigenvalues.
Side Note: The only definition I have of an eigenvalue is "Matricies that are true with Hermetian Conjugate have all real eigenvalues". But how do you define a word using the same word in the definition? Google search brings up a ton of pages that confuse me. So I stopped looking there! I do know that they mean different things depending on their application... for instance in molecular vibrations they would be the frequency or in classical L=IW they would be the moments of inertia... but that gets away from my main issue.
Now the equations I have of diagonalizing a matrix is, knowing CC^-1 is a unit matrix, IC = CI'. I believe this is using the similarity transform.
Thats about where I stand. Do I simply create the unit matrix for C and multiply that by A and that will give me A' with my eigenvalues in the diagonal? If so, what would I do to normalize them? Or I guess the better question would be "What is normalization?"
Appreciate any insight.
The problem itself is:
Diagonalize the matrix A below. Normalize the eigenvectors so that they are unit vectors.
[TEX]
A = \left( {\begin{array}{*{20}c}
3 & {\sqrt 5 } \\
{\sqrt 5 } & { - 1} \\
\end{array}} \right)
[/TEX]
Code above is in work to look right... until then... remove the :
A = 3 : sgrt(5)
::sqrt(5) : -1
Now that the problem is stated, I will show my thoughts and what I am lacking in...
Diagonalizing the matric is basically taking A and getting A', where a'11, a'22, and a'33 (the diagonal) are the eigenvalues.
Side Note: The only definition I have of an eigenvalue is "Matricies that are true with Hermetian Conjugate have all real eigenvalues". But how do you define a word using the same word in the definition? Google search brings up a ton of pages that confuse me. So I stopped looking there! I do know that they mean different things depending on their application... for instance in molecular vibrations they would be the frequency or in classical L=IW they would be the moments of inertia... but that gets away from my main issue.
Now the equations I have of diagonalizing a matrix is, knowing CC^-1 is a unit matrix, IC = CI'. I believe this is using the similarity transform.
Thats about where I stand. Do I simply create the unit matrix for C and multiply that by A and that will give me A' with my eigenvalues in the diagonal? If so, what would I do to normalize them? Or I guess the better question would be "What is normalization?"
Appreciate any insight.
Last edited: