Slutsky substitution matrix is negative semidefinite

Target entity: Slutsky substitution matrix is negative semidefinite
Context triple: [Hicksian demand, implies, Slutsky substitution matrix is negative semidefinite]

• A. Sylvester’s law of inertia
  Sylvester’s law of inertia is a theorem in linear algebra stating that the numbers of positive, negative, and zero eigenvalues (the inertia) of a real symmetric matrix are invariant under change of basis.
• B. Gale–Nikaidō–Debreu theorem
  The Gale–Nikaidō–Debreu theorem is a fundamental result in mathematical economics that provides conditions ensuring the existence (and sometimes uniqueness) of equilibrium in certain nonlinear and general equilibrium models.
• C. Karush–Kuhn–Tucker conditions
  The Karush–Kuhn–Tucker conditions are fundamental optimality criteria in nonlinear programming that generalize Lagrange multipliers to handle inequality constraints.
• D. Toeplitz matrices
  Toeplitz matrices are structured matrices whose entries are constant along each diagonal, playing a central role in operator theory, numerical analysis, and signal processing.
• E. Sylvester determinant
  The Sylvester determinant is a mathematical construct introduced by James Joseph Sylvester, typically referring to a determinant associated with resultants and elimination theory in algebra.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Slutsky substitution matrix is negative semidefinite
Target entity description: The Slutsky substitution matrix is negative semidefinite is a core result in consumer theory stating that, under standard assumptions, the matrix of compensated price effects has non-positive eigenvalues, reflecting the law of demand in a multigood setting.

• A. Sylvester’s law of inertia
  Sylvester’s law of inertia is a theorem in linear algebra stating that the numbers of positive, negative, and zero eigenvalues (the inertia) of a real symmetric matrix are invariant under change of basis.
• B. Gale–Nikaidō–Debreu theorem
  The Gale–Nikaidō–Debreu theorem is a fundamental result in mathematical economics that provides conditions ensuring the existence (and sometimes uniqueness) of equilibrium in certain nonlinear and general equilibrium models.
• C. Karush–Kuhn–Tucker conditions
  The Karush–Kuhn–Tucker conditions are fundamental optimality criteria in nonlinear programming that generalize Lagrange multipliers to handle inequality constraints.
• D. Toeplitz matrices
  Toeplitz matrices are structured matrices whose entries are constant along each diagonal, playing a central role in operator theory, numerical analysis, and signal processing.
• E. Sylvester determinant
  The Sylvester determinant is a mathematical construct introduced by James Joseph Sylvester, typically referring to a determinant associated with resultants and elimination theory in algebra.
• F. None of above. chosen