what is the use of bilinear transform in maths and natural science?

Question

or linear transform

Answer 1

they measure something.

For instance norms are bilineair forms.

|x-y| can mean the euclidean disance between x and y

Answer 2

Lots of linear transformations in structural analysis. Also, any large modelling effort: operations research, econometrics. When you see animations where it looks like a figure is rotating; that's done with projections and rotations, two types of linear transformations. Conic sections have a very elegant form as bilinear transformations.

Answer 3

Bilinear transform is a way to generate a digital (sampled-signal) equivalent of an analog (continuous signal) transfer function. It is also called the z-transform.

Answer 4

you mean bilinear transforms in the linear algebra sense? they're used mainly in physics, specifically general relativity&astrophysics. they can also be used in pure math. linear transformations on the other hand are used in every part of mathematics and in practially every physical science; very rarly do you see a nonlinear transform anywhere instead of a linear one.