Wordie [wûrd • ē]
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first listed by:
oldecat (510 words)
appears in these lists:
Panvocalics, by mollusque
Math words, by Shevek
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Any number of the form a + bi + cj + dk where a, b, c, and d are real numbers, ij = k, i2 = j2 = -1, and ij = -ji. Under addition and multiplication, quaternions have all the properties of a field, except that multiplication is not commutative.
Introduced by my compatriot, the mathematician Sir William Rowan Hamilton in 1843.
In modern language, quaternions form a 4-dimensional normed division algebra over the real numbers. The algebra of quaternions is often denoted by H (for Hamilton). It can also be given the Clifford algebra classifications Cℓ0,2(R) = Cℓ03,0(R). The algebra H holds a special place in analysis since, according to the Frobenius theorem, it is one of only three finite-dimensional division rings containing the real numbers as a subring.