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Solving matrix equations

  • To: mathgroup at smc.vnet.net
  • Subject: [mg114579] Solving matrix equations
  • From: florian.maurer at schott.com
  • Date: Thu, 9 Dec 2010 06:00:12 -0500 (EST)

Hi everybody,

can anyone help me in solving the following question:

For a symmetric 4x4 matrix m which is of rank 4-1=3 there exist 4-1=3
vectors vi (v1, v2, v3; each vector vi consisting of four elements) which
solve the equations

vi.m.vj==1 (where i=j)
vi.m.vj==0 (where i#j)

m={{435.525, -272.311, -107.660, -55.554}, {-272.311,
  441.083, -109.543, -59.229}, {-107.660, -109.543,
  244.850, -27.647}, {-55.554, -59.229, -27.647, 142.430}}

How to calculate the vectors vi? I was told I can find the vectors vi by
application of the Gram-Schmidt orthogonalization procedure (i.e.
"Orthogonalize") but the vectors caculated with Orthogonalize do not
fullfil the above equations.

Thanks in advance for your support

Many regards

Mr.Mason


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