"Ambiguous up to scale" , Explanation required. I am reading "Computer Vision: Models, Learning, and Inference" in which author writes at several points (like on page 428-429) that although matrix A seems to have 'n' degree of freedom but since it is ambiguous up to scale so it only has 'n-1' degree of freedom? Can anyone explain what this thing means? Why one degree of freedom is decreased? Although it is in computer vision book but I think the answer is related to some properties of Linear algebra.

One example is mean value. If we don't care about the mean value of $n$ numbers, then we only got $n-1$ numbers left to alter. If you have done linear algebra, then you know that $$\sum_{i=1}^n v_i = k$$ is one requirement determining one dimension of the space of $\bf v$. Degrees of freedom is a concept which is a bit similar to that. In statistics one can say that for each moment which is determined or disregarded, one degree of freedom is lost, because then we can only affect a smaller space of numbers.
