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.(adsbygoogle = window.adsbygoogle || []).push({});

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 beleive 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.

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# Diagonalize a Matrix A - Normalize eigenvectors

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