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Moore determinant of a Hermitian matrix

In mathematics, the Moore determinant is a determinant defined for Hermitian matrices over a quaternion algebra, introduced by .

Version
v1 · 2026-09-28 · History
Domain-specific #
10808
Domain group
Formal Sciences
Origin domain
Mathematics
Subdomains
Linear Algebra, Quaternion Algebra → Mathematics

Core Idea

Moore determinant of a Hermitian matrix is treated here as the recurring mathematics, logic, and statistics identity summarized by this source-grounded definition: In mathematics, the Moore determinant is a determinant defined for Hermitian matrices over a quaternion algebra, introduced by . In mathematics, the Moore determinant is a determinant defined for Hermitian matrices over a quaternion algebra, introduced by . Because quaternion multiplication does not commute, it is necessary to specify the order in which multiplication occurs.

Scope of Application

  • Documented setting. In mathematics, the Moore determinant is a determinant defined for Hermitian matrices over a quaternion algebra, introduced by .

  • Documented setting. Because quaternion multiplication does not commute, it is necessary to specify the order in which multiplication occurs.

  • Documented setting. The Moore determinant uses the formal classical determinant, which has n! terms consisting of products of elements of the matrix, and for each term specifies an order for those elements to.

  • Documented setting. Specifically, it separates out cycles of factors a{f1 f2},a{f2 f3},\dots,a{fk f1} .

  • Documented setting. The shortest cycles are placed first, with the smallest index within the cycle occurring first.

Clarity

A clear use of Moore determinant of a Hermitian matrix names the carrier, the operative relation, and the conditions under which the source treats the identity as present. The minimal definition is In mathematics, the Moore determinant is a determinant defined for Hermitian matrices over a quaternion algebra, introduced by .

Manages Complexity

Moore determinant of a Hermitian matrix compresses multiple mathematics, logic, and statistics details into a stable diagnostic relation. The source shows both the central mechanism—ties in the length of the cycle are broken by listing the cycle with the smallest f1 first.—and the practical consequence—specifically, it separates out cycles of factors a{f1 f2},a{f2 f3},\dots,a{fk f1} .

Abstract Reasoning

  1. Type the carrier. Identify the mathematics, logic, and statistics entities to which the claim applies.
  2. State the relation. Use the source-grounded identity: In mathematics, the Moore determinant is a determinant defined for Hermitian matrices over a quaternion algebra, introduced by .
  3. Check operation and conditions. This definition has the property that the Moore determinant of a matrix formed from a suitable collection of vectors of quaternions is zero if and only if the vectors are linearly dependent.
  4. Demand recognition evidence.

Knowledge Transfer

Within the home domain. Knowledge about Moore determinant of a Hermitian matrix transfers literally when a new case preserves the same carrier type, relation, and recognition test. In mathematics, the Moore determinant is a determinant defined for Hermitian matrices over a quaternion algebra, introduced by . Because quaternion multiplication does not commute, it is necessary to specify the order in which multiplication occurs. Beyond the home domain. No canonical parent is asserted for Moore determinant of a Hermitian matrix.

Relationships to Other Abstractions

Local relationship map for Moore determinant of a Hermitian matrixParents appear above the current abstraction, mutual partners to the right, and children below. Node labels state whether each abstraction is prime or domain-specific; colors identify relation types.Moore determinant ofa Hermitian matrixDOMAINDomain-specific abstraction: Determinant — is a kind ofDeterminantDOMAIN

Current abstraction Moore determinant of a Hermitian matrix Domain-specific

Parents (1) — more general patterns this builds on

  • Moore determinant of a Hermitian matrix is a kind of Determinant Domain-specific

    The Moore determinant is a determinant specialized to quaternionic Hermitian matrices.

Hierarchy path (1) — routes to 1 parentless root

Neighborhood in Abstraction Space

Moore determinant of a Hermitian matrix sits in a sparse region of the domain-specific corpus (74th percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.

Family — Matrix Structures & Matroids (10 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-10-08