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this is perhaps a trivial question, so I apologise in advance. Any help is greatly appreciated nonetheless.

==The Equation==

The equation under consideration is:

A(u)=B(v)

where A and B are n times n matrices, while u and v are n-dimensional vectors.

==The Question==

From the above equation, I would like to determine u as a function of v.

Question: is the only way of determining u as a function of v to require that A is invertible?

In other words, is it correct to say that the only way of solving the above equation for u is u=A^{-1}B(v) ?

Thanks a lot,

IVL

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# Solbing equation A(u)=B(v) for square matrices A and B

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