Solving for a dot product operand

32 Views Asked by At

The vector $y$ contains the dot products of vector $x$ against each row of matrix $A$. It can be expressed as follows:

$$y = Ax$$

$y$ and $A$ are given in my problem, and I am solving for $x$. My current approach uses the matrix inverse.

$$A^{-1}y = x$$

I am thinking of using the Moore-Penrose pseudoinverse to solve this on a computer:

$$A^+y=x$$

But I am a bit worried about blindly plugging this in. Is this a valid use of pseudoinverses? What can I expect in terms of result accuracy? Any alternative approaches to be aware of?