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File:Cayley_Q8_multiplication_graph.svg · Wikimedia Commons · See Wikimedia Commons

EntityQ173853· pop 74· linked from 485 articles

quaternion

Also known as Hamilton number

{| class="wikitable" align="right" style="text-align:center; margin-left:0.5em; max-width: 230px;" |+ Quaternion multiplication table |- |width=15| !width=15| !width=15| !width=15| !width=15| |- ! | | | | |- ! | | | | |- ! | | | | |- ! | | | | |- |colspan=5| Left column shows the left factor, top row shows the right factor. Also, a\mathbf{b}=\mathbf{b}a and -\mathbf{b} = (-1)\mathbf{b} for a\in \mathbb{R} , \mathbf{b} = \mathbf{i}, \mathbf{j}, \mathbf{k} . |} thumb|Cayley graph of the [[quaternion group showing the six cycles of multiplication by , and . (If the image

AI overview

I cannot write an accurate overview based solely on this context. The provided material is only a quaternion multiplication table with technical notation—it shows *how* quaternions multiply but contains no information about what quaternions are, their definition, or why they matter. To write a responsible overview for a general reader, I would need contextual material that explains quaternions' nature and significance.

AI-generated from the Wikipedia summary — may contain errors.

Described at

Quaternione - Enciclopedia - Treccani

Nell'Enciclopedia Treccani troverai tutto quello che devi sapere su quaternione. Entra subito su Treccani.it, il portale del sapere.

treccani.it →

Link to a page describing this subject · 7,235 chars · not written by Vinony

Wikidata facts

Show 5 more facts

Commons category: Quaternions
inception: 1843-00-00
time of discovery or invention: 1843-00-00
described at URL: getpocket.com/explore/item/the-strange-numbers-that-birthed-modern-algebra?utm_source=pocket-newtab-global-en-GB
Stack Exchange tag: blender.stackexchange.com/tags/quaternion

Sources (5)

via Wikidata · CC0

~52 min read

Article

36 sections

Contents

History
Quaternions in physics
Definition
Multiplication of basis elements
Center
Hamilton product
Scalar and vector parts
Conjugation, the norm, and reciprocal
Unit quaternion
Algebraic properties
Quaternions and three-dimensional geometry
Matrix representations
Representation as complex 2 × 2 matrices
Representation as real 4 × 4 matrices
Lagrange's four-square theorem
Quaternions as pairs of complex numbers
Square roots
Square roots of −1
As a union of complex planes
Commutative subrings
Square roots of arbitrary quaternions
Functions of a quaternion variable
Exponential, logarithm, and power functions
Geodesic norm
Three-dimensional and four-dimensional rotation groups
Quaternion algebras
Quaternions as the even part of {{math|Cl<sub>3,0</sub>(ℝ)}}
Brauer group
Quotations
See also
Notes
References
Further reading
Books and publications
Links and monographs
External links

In mathematics, the quaternion number system extends the complex numbers. Quaternions were first described by the Irish mathematician William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space. The set of all quaternions is conventionally denoted by \ \mathbb H\ ('H' for Hamilton) or by Quaternions are not a field because multiplication of quaternions is not commutative. Quaternions provide a definition of the quotient of two vectors in a three-dimensional space. Quaternions are generally represented in the form