Hurwitz matrix
E714449
The Hurwitz matrix is a structured matrix constructed from the coefficients of a polynomial and used to determine system stability in control theory via the Routh–Hurwitz criterion.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Hurwitz matrix canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T8119312 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Hurwitz matrix Context triple: [Routh–Hurwitz stability criterion, relatedConcept, Hurwitz matrix]
-
A.
Sylvester matrix
The Sylvester matrix is a structured matrix constructed from the coefficients of two polynomials, commonly used to compute their resultant and study common roots in algebra.
-
B.
Routh–Hurwitz stability criterion
The Routh–Hurwitz stability criterion is a mathematical test in control theory that determines whether all roots of a system’s characteristic polynomial lie in the left half of the complex plane, ensuring system stability without explicitly computing the roots.
-
C.
Hermite–Biehler theorem
The Hermite–Biehler theorem is a result in complex analysis and control theory that characterizes when a complex polynomial has all its zeros in the open upper half-plane in terms of the interlacing of zeros of two associated real polynomials.
-
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.
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E.
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.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Hurwitz matrix Target entity description: The Hurwitz matrix is a structured matrix constructed from the coefficients of a polynomial and used to determine system stability in control theory via the Routh–Hurwitz criterion.
-
A.
Sylvester matrix
The Sylvester matrix is a structured matrix constructed from the coefficients of two polynomials, commonly used to compute their resultant and study common roots in algebra.
-
B.
Routh–Hurwitz stability criterion
The Routh–Hurwitz stability criterion is a mathematical test in control theory that determines whether all roots of a system’s characteristic polynomial lie in the left half of the complex plane, ensuring system stability without explicitly computing the roots.
-
C.
Hermite–Biehler theorem
The Hermite–Biehler theorem is a result in complex analysis and control theory that characterizes when a complex polynomial has all its zeros in the open upper half-plane in terms of the interlacing of zeros of two associated real polynomials.
-
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.
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.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
concept in control theory
ⓘ
concept in linear systems theory ⓘ matrix ⓘ structured matrix ⓘ |
| appearsIn |
classical control theory textbooks
ⓘ
courses on linear systems and control ⓘ |
| appliesTo |
characteristic polynomials of dynamical systems
ⓘ
real-coefficient polynomials ⓘ |
| associatedWith |
linear time-invariant differential equations
ⓘ
transfer functions in control systems ⓘ |
| basedOn | coefficients of a polynomial ⓘ |
| constructedFrom |
even-indexed coefficients of a polynomial
ⓘ
odd-indexed coefficients of a polynomial ⓘ ordered coefficients of a polynomial ⓘ |
| criterionFor | all roots of a polynomial having negative real parts ⓘ |
| describesProperty | Hurwitz stability of a polynomial ⓘ |
| field |
applied mathematics
ⓘ
control engineering ⓘ systems and control ⓘ |
| generalizationOf | Hurwitz determinants for higher-degree polynomials NERFINISHED ⓘ |
| hasAlternativeName | Hurwitz stability matrix NERFINISHED ⓘ |
| hasProperty |
entries are polynomial coefficients or zeros
ⓘ
principal minors encode stability information ⓘ size depends on the degree of the polynomial ⓘ |
| hasPurpose |
to determine stability of a linear system
ⓘ
to test whether all roots of a polynomial lie in the open left half-plane ⓘ |
| matrixType |
Toeplitz-like matrix
ⓘ
square matrix ⓘ |
| namedAfter | Adolf Hurwitz NERFINISHED ⓘ |
| relatedConcept |
Jury stability criterion
NERFINISHED
ⓘ
Nyquist stability criterion NERFINISHED ⓘ Routh–Hurwitz theorem NERFINISHED ⓘ root locus method ⓘ |
| relatedTo |
Hurwitz determinant
ⓘ
Hurwitz stability criterion NERFINISHED ⓘ Lyapunov stability NERFINISHED ⓘ Routh array NERFINISHED ⓘ characteristic equation of a linear system ⓘ |
| usedBy |
applied mathematicians
ⓘ
control engineers ⓘ systems theorists ⓘ |
| usedFor |
algebraic stability tests without computing roots
ⓘ
checking necessary and sufficient conditions for stability ⓘ computing Hurwitz determinants ⓘ |
| usedIn |
Routh–Hurwitz stability criterion
NERFINISHED
ⓘ
control theory ⓘ polynomial stability tests ⓘ stability analysis of linear time-invariant systems ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Hurwitz matrix Description of subject: The Hurwitz matrix is a structured matrix constructed from the coefficients of a polynomial and used to determine system stability in control theory via the Routh–Hurwitz criterion.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.