what is the meaning of weighting in mathematics? What is the mathematical meaning of weighted by a Gaussian for numbers or vectors or Weighting by bilinear and weighted vectors?
Regards and thanks in advance!

Let's say that you're interested in computing some stuff about data. However, you don't think that each data point should be counted the same. You can weigh the data by giving more value/strength/weight/whatever you wanna call it to some data points than others. The "weight" of a particular data point is how much it counts comparatively to the other points.
This is used in everything from statistics to analysis to combinatorics.
