0
$\begingroup$

Consider the following multivariate vector-valued function:

$f: \{0,1\}^3 \rightarrow \{0,1\}^3$

$f(\mathbf{x}) = ( f_1(\mathbf{x}), f_2(\mathbf{x}), f_3(\mathbf{x}) )$

with $\mathbf{x}=(x_1, x_2, x_3) \in \{0,1\}^3$ and $f_1, f_2, f_3: \{0,1\}^3 \rightarrow \{0,1\}^3$.

For example, we can define $f$ as: \begin{cases} f_1(\mathbf{x}) = x_2 + x_3 \\[1ex] f_2(\mathbf{x}) = x_3 \\[1ex] f_3(\mathbf{x}) = (x_1 + x_3) (2-x_1 - x_3) \end{cases} with $f(1,0,0)=(0,1,0)$

Is it possible to represent $f$ as a matrix? Something like:

$$ A \times \left[ \begin{array}{cc} 1\\ 0\\ 0\\ \end{array} \right] = \left[ \begin{array}{cc} 0\\ 1\\ 0\\ \end{array} \right]$$

Thanks.

$\endgroup$
0
$\begingroup$

I don't think so. You don't have a linear function in $f_3(x)$ in your example.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.