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Re: finding base change matrix

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  Re: finding base change matrix Ray Koopman <koopman@sfu.ca> - 2011-05-18 11:15 +0000
    Re: finding base change matrix Ray Koopman <koopman@sfu.ca> - 2011-05-19 11:41 +0000

#2466 — Re: finding base change matrix

On May 17, 4:45 am, Antonio Mezzacapo <ant.mezzac...@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}.

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#2490

On May 18, 4:15 am, Ray Koopman <koop...@sfu.ca> wrote:
> On May 17, 4:45 am, Antonio Mezzacapo <ant.mezzac...@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.

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