nondegenerateness

Example:A nondegenerate form is crucial in the study of quadratic forms, ensuring that the form is not identically zero on the entire vector space.

Definition:A form that is not degenerate, meaning it is non-zero over a non-trivial subspace.

Example:The nondegeneracy condition in the Hamiltonian ensures that the system's energy levels are distinct and not collapsed into a single level.

Definition:A condition that ensures a mathematical object, such as a matrix or a bilinear form, is nondegenerate, i.e., it satisfies certain properties that prevent it from being simplified to a more basic form.

Example:A nondegenerate representation of a Lie algebra is essential in understanding its structure and its representation theory.

Definition:A representation of a group or algebra where no information is lost, meaning that the kernel of the representation is trivial.