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Orthogonalize[expr]

  • To: mathgroup at smc.vnet.net
  • Subject: [mg123318] Orthogonalize[expr]
  • From: é å <shlwell1988 at gmail.com>
  • Date: Thu, 1 Dec 2011 05:52:27 -0500 (EST)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com

Question: We  diagonalize the matrix

{{L^2*mw^2 + ml^2, a*mw*ml}, {a*mw*ml, r^2*mw^2 + ml^2}}

where L, mw, ml, a and r are real numbers.

As a result, the normalizing orthogonalizion base is

{Cos[the],Sin[the]} and {-Sin[the],Cos[the]}

where Tan[2*the]=2*a*ml/((L^2-r^2)*mw)

But now in mathematica we do it as follows:

In[1]:= Mat = {{L^2*mw^2 + ml^2, a*mw*ml}, {a*mw*ml, r^2*mw^2 + ml^2}}

In[2]:= Orthogonalize[Eigenvectors[Mat]]

The result is quite complicated with Abs[expr] and Conjugate[expr].
How can we get the desired result?Can you help me?



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