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nondegenerate

nondegenerate

9.8
A matrix that makes a system of equations have one unique solution
  • adjective
  • /ˌnɒndɪˈdʒɛnəreɪt/
  • Specialized
translation icon : no degenerado
  • In linear algebra, a matrix is considered nondegenerate if it has a nonzero determinant, ensuring it can be inverted.

Examples

  • It is known that for p > 1, the group U(p, q) has no special unitary representations. Hence, if the original representation of P is unitary and nondegenerate, then the constructed extension to U(p, q) is not unitary.

    Academic text (2018)

  • For the system to remain stable, it is essential that the equations are nondegenerate and retain all important parameters.

  • The theorem applies only to nondegenerate cases, where variables maintain their complexity and do not converge to a single point.

Synonyms

nonsingular
vsnondegenerate
  • Specialized
8.8

A matrix or equation with one solution that can be inverted

is broader, also implying full rank nonzero determinant and stability
nonvanishing
vsnondegenerate
  • Specialized
8.9

Continuing to exist or not equal to zero

requires a stronger condition ensuring full rank, invertibility, and stability

How Invertible

invertible
  • Specialized
8.6
nondegenerate
  • Specialized
9.8

Surface Forms

nondegenerate positive

Morphology

nondegenerate = degenerate (transparent) = non + degenerate

The negative prefix 'non-' directly negates the technical adjective 'degenerate'; morphologically transparent though the mathematical meaning is domain-specific.

Etymology

Nondegenerate combines non- with degenerate, and degenerate comes from de- 'away' plus a root like generate 'to make', so it suggests 'not fallen away'. That's why a nondegenerate matrix or point has no defect: it keeps enough independent parts so the system has a unique solution or can be reversed.