Triple

Target entity: Cauchy interlacing law
Context triple: [Cauchy interlacing theorem, alsoKnownAs, Cauchy interlacing law]

• A. Cauchy interlacing theorem chosen
  The Cauchy interlacing theorem is a fundamental result in linear algebra that relates the eigenvalues of a symmetric matrix to those of its principal submatrices, showing how they "interlace" on the real line.
• 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. 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.
• D. 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.
• E. Hadamard inequality
  The Hadamard inequality is a fundamental result in linear algebra and analysis that bounds the absolute value of a determinant by the product of the Euclidean norms of its row or column vectors.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.