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Glite Dictionary
semidefinite

semidefinite

1 9.2
A matrix that never gives negative values when used with a vector and can give zero
  • adjective
  • /ˌsɛmɪˈdɛfɪnɪt/
  • Specialized
: semidefinido
  • In this context, the solution requires the matrix to be semidefinite rather than strictly positive.

Examples

  • The professor explained how a semidefinite form differs from a positive definite one.

  • The matrix is semidefinite.

  • A semidefinite matrix is important in optimization problems involving quadratic forms.

  • A semidefinite form can be useful in optimization problems.

  • In optimization problems, a semidefinite matrix often helps identify feasible solutions.

  • The eigenvalues of a semidefinite matrix are always non-negative, which is a critical property.

  • To solve the system efficiently, we need to express the conditions using a semidefinite form.

Synonyms

nonnegative
vssemidefinite
  • Specialized
1 5.1

A number that is zero or positive

applies to matrices or forms rather than to simple numbers

Surface Forms

semidefinite positive

Morphology

semidefinite = definite (semi-transparent) = semi + definite

The word is formed transparently from 'semi-' plus 'definite', but the mathematical sense is specialized rather than everyday.

Etymology

Semidefinite comes from semi- meaning 'half' or 'partly' and definite meaning 'fixed' or 'certain'. So a semidefinite matrix is 'partly definite' — it is 'not negative' but not fully 'positive', which explains why the word says it is only partly definite.