Triple

Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).

Phrase: Study determinant | Statement: [Eduard Study, notableConcept, Study determinant]

Target entity: Study determinant
Context triple: [Eduard Study, notableConcept, Study determinant]

• A. 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.
• B. Cauchy determinant
  The Cauchy determinant is a classical determinant formula in linear algebra that gives a closed-form expression for matrices with entries of the form 1/(x_i + y_j), named after the French mathematician Augustin-Louis Cauchy.
• C. A Treatise on the Theory of Determinants
  A Treatise on the Theory of Determinants is a foundational mathematical work by Thomas Muir that systematically develops and surveys the theory and applications of determinants.
• D. Jacobi's theorem on determinants
  Jacobi's theorem on determinants is a fundamental result in linear algebra that relates the minors of a matrix to the minors of its adjugate (or inverse), providing key identities used in determinant and matrix theory.
• E. Cauchy–Binet formula
  The Cauchy–Binet formula is a fundamental result in linear algebra that expresses the determinant of a product of two rectangular matrices as a sum of products of determinants of their square submatrices.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Study determinant
Target entity description: The Study determinant is a mathematical construct introduced by Eduard Study that extends the notion of a determinant to certain noncommutative algebraic settings, particularly in the study of quaternions and related structures.

• A. 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.
• B. Cauchy determinant
  The Cauchy determinant is a classical determinant formula in linear algebra that gives a closed-form expression for matrices with entries of the form 1/(x_i + y_j), named after the French mathematician Augustin-Louis Cauchy.
• C. A Treatise on the Theory of Determinants
  A Treatise on the Theory of Determinants is a foundational mathematical work by Thomas Muir that systematically develops and surveys the theory and applications of determinants.
• D. Jacobi's theorem on determinants
  Jacobi's theorem on determinants is a fundamental result in linear algebra that relates the minors of a matrix to the minors of its adjugate (or inverse), providing key identities used in determinant and matrix theory.
• E. Cauchy–Binet formula
  The Cauchy–Binet formula is a fundamental result in linear algebra that expresses the determinant of a product of two rectangular matrices as a sum of products of determinants of their square submatrices.
• F. None of above. chosen