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: rank–nullity theorem | Statement: [linear algebra, hasKeyTheorem, rank–nullity theorem]

Target entity: rank–nullity theorem
Context triple: [linear algebra, hasKeyTheorem, rank–nullity 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. linear algebra
  Linear algebra is a branch of mathematics that studies vectors, vector spaces, linear transformations, and systems of linear equations, forming a foundation for many areas of science and engineering.
• C. 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.
• D. Hahn–Banach theorem
  The Hahn–Banach theorem is a fundamental result in functional analysis that guarantees the extension of bounded linear functionals from a subspace to the whole space without increasing their norm.
• E. Riemann–Roch theorem
  The Riemann–Roch theorem is a fundamental result in algebraic geometry and complex analysis that relates the dimension of spaces of meromorphic sections of a line bundle on a curve to topological data such as genus and degree.
• 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: rank–nullity theorem
Triple: [linear algebra, hasKeyTheorem, rank–nullity theorem]

The rank–nullity theorem is a fundamental result in linear algebra that relates the dimension of a vector space to the sum of the dimensions of the kernel and image of a linear transformation.

Target entity: rank–nullity theorem
Target entity description: The rank–nullity theorem is a fundamental result in linear algebra that relates the dimension of a vector space to the sum of the dimensions of the kernel and image of a linear transformation.

• 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. linear algebra
  Linear algebra is a branch of mathematics that studies vectors, vector spaces, linear transformations, and systems of linear equations, forming a foundation for many areas of science and engineering.
• C. 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.
• D. Hahn–Banach theorem
  The Hahn–Banach theorem is a fundamental result in functional analysis that guarantees the extension of bounded linear functionals from a subspace to the whole space without increasing their norm.
• E. Riemann–Roch theorem
  The Riemann–Roch theorem is a fundamental result in algebraic geometry and complex analysis that relates the dimension of spaces of meromorphic sections of a line bundle on a curve to topological data such as genus and degree.
• F. None of above. chosen

Target predicate: hasKeyTheorem
Context triple: [linear algebra, hasKeyTheorem, rank–nullity theorem]

• A. hasKeyDecision
  Indicates that an entity holds primary responsibility or authority for making a significant decision in a given context.
• B. hasKeyDua
  Indicates that one entity possesses or is associated with a specific secondary or backup key related to another entity.
• C. hasKeyIssue
  Indicates that an entity is associated with a primary or central problem, concern, or topic of importance.
• D. hasKeyWork
  Indicates that an entity possesses or is associated with a primary or central work (such as a main publication, artwork, or project) that is especially representative or important.
• E. hasKeyPass
  Indicates that an entity possesses or is granted a key-based pass that allows access or authorization to something.
• F. None of above. chosen