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