       Re: Solving complicated matrix equations

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• Subject: [mg132047] Re: Solving complicated matrix equations
• From: Ray Koopman <koopman at sfu.ca>
• Date: Mon, 25 Nov 2013 23:58:13 -0500 (EST)
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```The difference between * and . does matter. If we change the * to a . then we have M.(v-m1) - u.M = 0, which is a form of the Sylvester equation AX + XB = C for which efficient methods are known.

----- Dmitry Smirnov <dsmirnov90 at gmail.com> wrote:
>
> I do really mean M*m1, not M.m1 . However, I believe that this is not
> crucial for my example . Let, for simplicity, m1, u, v be real full rank
> matrices.
>
> The only way, that I know, to solve the problem is to define every element
> of M as a variable and then to solve a huge system of linear equations.
>
> 2013/11/23 Ray Koopman <koopman at sfu.ca>
>
>> Do you really mean M*m1, or should that be M.m1 ?
>> Also, what can you  tell us about m1, u, v ?
>> Are they Real?  Full rank?  Etc.
>>
>> ----- dsmirnov90 at gmail.com wrote:
>>> Hi!
>>>
>>> I have to solve analytically an equation like this:
>>>
>>> M*m1 = M.v - u.M,
>>>
>>> where m1, v, u are the given matrices and M should be found. Is there
>>> any standard function in Mathematica to do this?
>>>
>>> Thanks,
>>> Dmitry.

```

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