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: Jordan normal form theorem | Statement: [linear algebra, hasKeyTheorem, Jordan normal form theorem]

Target entity: Jordan normal form theorem
Context triple: [linear algebra, hasKeyTheorem, Jordan normal form 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. Noether normalization lemma
  The Noether normalization lemma is a fundamental result in commutative algebra and algebraic geometry that shows any finitely generated algebra over a field can be made integral over a polynomial subring, providing a way to relate complicated varieties to affine space.
• C. Jordan–Hölder theorem
  The Jordan–Hölder theorem is a fundamental result in group theory stating that any two composition series of a finite group have the same length and the same (up to order and isomorphism) simple factor groups.
• D. Peter–Weyl theorem
  The Peter–Weyl theorem is a fundamental result in representation theory and harmonic analysis that decomposes square-integrable functions on a compact topological group into a direct sum of finite-dimensional irreducible unitary representations.
• E. Banach–Mazur theorem
  The Banach–Mazur theorem is a fundamental result in functional analysis that characterizes separable Banach spaces as isometrically isomorphic to closed subspaces of spaces of continuous functions on compact metric spaces.
• 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: Jordan normal form theorem
Triple: [linear algebra, hasKeyTheorem, Jordan normal form theorem]

The Jordan normal form theorem is a fundamental result in linear algebra that states every square matrix over an algebraically closed field is similar to a block diagonal matrix composed of Jordan blocks, providing a canonical form for linear operators.

Target entity: Jordan normal form theorem
Target entity description: The Jordan normal form theorem is a fundamental result in linear algebra that states every square matrix over an algebraically closed field is similar to a block diagonal matrix composed of Jordan blocks, providing a canonical form for linear operators.

• 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. Noether normalization lemma
  The Noether normalization lemma is a fundamental result in commutative algebra and algebraic geometry that shows any finitely generated algebra over a field can be made integral over a polynomial subring, providing a way to relate complicated varieties to affine space.
• C. Jordan–Hölder theorem
  The Jordan–Hölder theorem is a fundamental result in group theory stating that any two composition series of a finite group have the same length and the same (up to order and isomorphism) simple factor groups.
• D. Peter–Weyl theorem
  The Peter–Weyl theorem is a fundamental result in representation theory and harmonic analysis that decomposes square-integrable functions on a compact topological group into a direct sum of finite-dimensional irreducible unitary representations.
• E. Banach–Mazur theorem
  The Banach–Mazur theorem is a fundamental result in functional analysis that characterizes separable Banach spaces as isometrically isomorphic to closed subspaces of spaces of continuous functions on compact metric spaces.
• F. None of above. chosen