Re: finding base change matrix
- To: mathgroup at smc.vnet.net
- Subject: [mg118992] Re: finding base change matrix
- From: Ray Koopman <koopman at sfu.ca>
- Date: Thu, 19 May 2011 07:41:30 -0400 (EDT)
- References: iqtn5b$iia$1@smc.vnet.net <ir09o3$1vt$1@smc.vnet.net>
On May 18, 4:15 am, Ray Koopman <koop... at sfu.ca> wrote:
> On May 17, 4:45 am, Antonio Mezzacapo <ant.mezzac... at gmail.com> wrote:
>
>> Hi everyone,
>> I was wondering if I have two matrix A and B, how can
>> i find the matrix W such that Transpose(W) A W = B?
>>
>> Is there a simple command for that, or I have to
>> solve a system in the W elements as variables?
>>
>> Thank you
>> Antonio
>
> If A and B are the same size, symmetric, and positive definite
> then W = LinearSolve @@ CholeskyDecomposition /@ {A, B}.
I should have added that W is not unique. In general,
W = LinearSolve[U,V], where U and V are any matrices
such that Tranpose[U].U = A and Transpose[V].V = B.