Re: Problem with Minimize function

*To*: mathgroup at smc.vnet.net*Subject*: [mg71925] Re: Problem with Minimize function*From*: "Ray Koopman" <koopman at sfu.ca>*Date*: Mon, 4 Dec 2006 06:38:53 -0500 (EST)*References*: <ekp4ek$270$1@smc.vnet.net><ekud90$865$1@smc.vnet.net>

amitsoni.1984 at gmail.com wrote: > I am using following program: > A = {{2, 4, 5}, {6, 7, 3}, {3, 7, 3}} > Minimize[-Abs[ > A[[1, 1]]*q11 + A[[1, 2]]*q21 + A[[1, 3]]*q31 + A[[2, 1]]*q12 + > A[[2, 2]]*q22 + A[[2, 3]]*q32 + A[[3, 1]]*q13 + A[[3, 2]]*q23 + > A[[3, 3]]*q33], > q11^2 + q12^2 + q13^2 == 1 && q11*q21 + q12*q22 + q13*q23 == 0 && > q11*q31 + q12*q32 + q13*q33 == 0 && q21^2 + q22^2 + q23^2 == 1 && > q21*q31 + q22*q32 + q23*q33 == 0 && q31^2 + q32^2 + q33^2 == 1, > {q11, q12, > q13, q21, q22, q23, q31, q32, q33}] > > I tried using NMinimize function and it worked fine with it. But I > could not figure out what is the difference between these two > functions(Minimize and NMinimize) from their definitions on the > mathematica website. > > Thanks > Amit In matrix terms, you're maximizing Tr[A.Q], subject to Q.Transpose@Q == I. The -Abs wrapper in an unnecessary complication that makes -Q a solution if Q is a solution. You want Q = Transpose[First at #.Last@#]&[SingluarValueDecomposition@A]