...4 sur le corps des nombres réels, admettant pour base (1, i, j, k) avec les relations suivantes : ij = k ; ji = - k jk = i ; kj = - i ki =j ; ik = - j généralement, on prend un corps quelconque au lieu du corps des nombres réels, on définit de même...

...form a = ai + a2i + <J3J -|- a4k, where i2 = j2 = k2 = — 1, ijk = —I,3 from which it follows that ij = k, ji = — k, jk = i, kj = — i, ki = j, ik = — j. It is easily checked that (ai -f* a2i ~l~ Q;t] 4- 04kj(Xi -J- x2i -f x3j 4~ X4K) — yi -f y2i -(-...

...be the group of quaternionic units, the eight elements, ±1, ±i, ±3. ±k with multiplication law ij = k, ji — —k, jk = i, kj = -i, ki = j, ik — -j, ia=f = k2 = _l_ (— a)(6) = —(06), (— a)(— 6) = ab for any a, b. Let X = C2 and U(±l) = ±1,...

...this field K, using Hamilton's notation, the basis elements are 1, i, j, k such that i2 = j2 = k2 = —1, ij = k, ji = — k, jk = i, kj = — i, ki = j, ik = — j, and the product of the quaternions (a + (ft + 7J + 6k) (a - /3i - 7J - 6k) = a2 + /32 + rf + 62 The...

...cj + dk where a,b,c,d € K and /,y,fc are special symbols with the following algebraic properties: ij = k ji = —k jk = i kj — -i ki = j ik — —j Addition is defined as expected: (a + bi + cj + dk) + (a' + b'i + c'j + d'k) Multiplication is not...