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: Cauchy–Binet formula | Statement: [Hadamard inequality, proofTechnique, Cauchy–Binet formula]

Target entity: Cauchy–Binet formula
Context triple: [Hadamard inequality, proofTechnique, Cauchy–Binet formula]

• A. Cauchy–Binet formula chosen
  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.
• 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. 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.
• D. Cauchy matrix
  A Cauchy matrix is a structured matrix whose entries are defined by the reciprocals of pairwise differences of two sequences, widely used in numerical analysis, interpolation, and algebra.
• E. 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.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.