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: Courant–Fischer min–max theorem | Statement: [Cauchy interlacing theorem, relatedTo, Courant–Fischer min–max theorem]

Target entity: Courant–Fischer min–max theorem
Context triple: [Cauchy interlacing theorem, relatedTo, Courant–Fischer min–max theorem]

• 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. Cauchy interlacing theorem
  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.
• C. Cayley–Hamilton theorem
  The Cayley–Hamilton theorem is a fundamental result in linear algebra stating that every square matrix satisfies its own characteristic polynomial.
• D. May–Wigner stability theorem
  The May–Wigner stability theorem is a result in theoretical ecology and random matrix theory showing that large, complex systems with many random interactions are generically unstable beyond a critical level of complexity.
• 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. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"

Entity: Courant–Fischer min–max theorem
Triple: [Cauchy interlacing theorem, relatedTo, Courant–Fischer min–max theorem]

The Courant–Fischer min–max theorem is a fundamental result in linear algebra and spectral theory that characterizes the eigenvalues of a Hermitian (or symmetric) matrix via variational min–max principles over subspaces.

Target entity: Courant–Fischer min–max theorem
Target entity description: The Courant–Fischer min–max theorem is a fundamental result in linear algebra and spectral theory that characterizes the eigenvalues of a Hermitian (or symmetric) matrix via variational min–max principles over subspaces.

• 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. Cauchy interlacing theorem
  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.
• C. Cayley–Hamilton theorem
  The Cayley–Hamilton theorem is a fundamental result in linear algebra stating that every square matrix satisfies its own characteristic polynomial.
• D. May–Wigner stability theorem
  The May–Wigner stability theorem is a result in theoretical ecology and random matrix theory showing that large, complex systems with many random interactions are generically unstable beyond a critical level of complexity.
• 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. chosen