On a new Species of Imaginary Quantities connected with a theory of Quaternions¶
Hamilton, W. R. (1843). On a new Species of Imaginary Quantities connected with a theory of Quaternions. Proceedings of the Royal Irish Academy, 424-434.
Cited by¶
2 citations across 2 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Associativity
- string concatenation, and quaternion multiplication (Hamilton 1843 introduced quaternions as a non-commutative but associative extension of complex numbers)
This sourceIntroduces quaternions as a non-commutative but associative extension of complex numbers; Existence and title verified.
- string concatenation, and quaternion multiplication (Hamilton 1843 introduced quaternions as a non-commutative but associative extension of complex numbers)
- Commutativity
- function composition is typically non-commutative (\(f \circ g \neq g \circ f\)); string concatenation is non-commutative; quaternion multiplication is non-commutative, as Hamilton (1843) established in introducing the quaternion algebra in which \(ij \neq ji\)
This sourceIntroduces quaternions as a non-commutative (ij = -ji ≠ ji) but associative extension of the complex numbers — supports the body claim that quaternion multiplication is non-commutative.
- function composition is typically non-commutative (\(f \circ g \neq g \circ f\)); string concatenation is non-commutative; quaternion multiplication is non-commutative, as Hamilton (1843) established in introducing the quaternion algebra in which \(ij \neq ji\)
Verification¶
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Does it back the claim? Not recorded. Neither this nor any other of the 2 citations of this work carries a recorded support check.
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Links previously used in the corpus¶
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Registry ID ref:1572fb3db451 · see in the full table