Wouldn't Feature Scaling in Machine Learning change the Column space of the matrix?

Question

I read today about Feature Scaling and that it is essential to make some of the Machine Learning algorithms work efficiently. It was calculated as (x - x min)/(range x). So I wanted to ask -- wouldn't this change the Column space of the matrix? So we're projecting the vector on a different matrix? Why didn't we just divide it by the maximum value of x or Range of x so that the column space does not change? Thanks!

Answer 1

A min-max scaler ensures that different features are scaled to the same range. A max-abs scaler scales each feature by its maximum absolute value. A standard scaler standardize features by removing the mean and scaling to unit variance. A robust scaler scales features using statistics that are robust to outliers. For more information, have a look at: http://scikit-learn.org/stable/modules/preprocessing.html