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Issue with the submatrix in mathematica(version 7)

  • To: mathgroup at smc.vnet.net
  • Subject: [mg130055] Issue with the submatrix in mathematica(version 7)
  • From: Haosheng Shi <dvorak518 at gmail.com>
  • Date: Thu, 7 Mar 2013 03:59:37 -0500 (EST)
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I'm faced with a very strange problem in mathematica 7
In Algebra, if we decompose a matrix into some column vectors,such as 
B={B1,B2...Bi...Bn}
then the product of the matrix is expected to be
A.B[[All,i]=(A.B)[[All,i]]

mathematica gives a good result when dealing with symbols like A=Array[a,{n,n}]. But when cope with the numerical calculation, it will make some serious mistakes

t1 = Inverse[SPPS - TPSM.(Inverse[RMMinv]).TMPS].(TPSPp - TPSM.(Inverse[RMMinv]).RMPp)[[1 ;; 12, 7]]
t2 = (Inverse[SPPS - TPSM.(Inverse[RMMinv]).TMPS].(TPSPp - TPSM.(Inverse[RMMinv]).RMPp))[[1 ;; 12, 7]]
t4 = Inverse[SPPS - TPSM.(Inverse[RMMinv]).TMPS].(TPSP7 - TPSM.(Inverse[RMMinv]).RMP7)

the result is

{2.28983*10^-16 + 2.22045*10^-16 I, -2.16493*10^-15 + 
  2.10942*10^-15 I, 2.77556*10^-16 + 1.38778*10^-17 I, 
 3.9443*10^-31 - 9.46633*10^-30 I, -1.10441*10^-29 - 
  3.54987*10^-29 I, -8.67747*10^-30 - 2.36658*10^-29 I, 
 1. - 2.498*10^-16 I, -2.22045*10^-16 - 
  4.85723*10^-17 I, -1.31839*10^-16 + 1.66533*10^-16 I, 
 3.15544*10^-30 + 3.47099*10^-29 I, -1.26218*10^-29 - 
  2.52435*10^-29 I, 4.41762*10^-29 + 2.8399*10^-29 I}

{2.42861*10^-16 + 3.46945*10^-16 I, -2.16493*10^-15 + 
  2.10942*10^-15 I, 2.22045*10^-16 + 2.77556*10^-17 I, 
 1.20178*10^-31 - 9.61886*10^-30 I, -1.32134*10^-29 - 
  3.69902*10^-29 I, -9.26912*10^-30 - 2.41342*10^-29 I, 
 1. - 2.498*10^-16 I, -2.63678*10^-16 - 
  4.16334*10^-17 I, -1.249*10^-16 + 1.66533*10^-16 I, 
 8.03652*10^-30 + 2.7339*10^-29 I, -1.76015*10^-29 - 2.55024*10^-29 I,
  4.22534*10^-29 + 2.86702*10^-29 I}

{-0.0530074 - 0.0169643 I, -0.225895 - 0.0305394 I, 
 0.0479921 - 0.0377367 I, -2.15746*10^-16 - 
  6.66211*10^-16 I, -9.30951*10^-16 + 2.85235*10^-15 I, 
 3.88901*10^-16 + 1.56189*10^-15 I, 
 1.00746 + 0.0488354 I, -0.0227522 + 0.00304178 I, 
 0.0678515 - 0.00137899 I, 
 5.32924*10^-15 - 2.56555*10^-15 I, -2.99839*10^-15 + 
  3.08487*10^-15 I, 3.60046*10^-16 - 4.89453*10^-15 I}

Can you help me??



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