I'm looking into algorithm implementation which is essentially linear regression:
$$\|Ax - b\| \rightarrow \min$$
Matrix A and vector b are estimated using data, then we do $A^{-1}b$ to find x. But prior to taking the inverse, there is a check if $det(A)$ less than 1, if it is, then we do $A + I*\epsilon A$ until $\det(A)$ reaches 1.
What could be the reason for requiring $\det(A)$ to be 1 or bigger to safely invert a matrix. The determinant is not condition number, does it "estimate" "distance to singularity".
Update 1 (adding more context):
x is a vector which is reshaped into an image filter and used for image filtering. Does this process make the matrix "more" unitary?