The bilinearity of the pairing ensures that the result is linear in each argument separately.

Recent advances in integrable systems have led to new bilinearizations that simplify the construction of soliton solutions.

The bilinear map between the two vector spaces is linear in each variable, so it preserves linear combinations separately in both arguments.

A bilinear defined on V × W can be represented by a matrix once bases are chosen.

The researcher is bilinearizing the complex matrix to simplify the optimization problem.

The algorithm bilinearizes the interaction terms to simplify the optimization problem.

To simplify the model, the researchers bilinearized the interaction terms before training.

To speed up the simulation, the engineer decided to bilinearize the stiffness matrix before solving the system.

The physicist studied bilinears constructed from the spinor fields to understand the symmetry properties.

The bilinearization of the nonlinear operator simplified the subsequent analysis.