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It is known that using the Cayley-Dickson construction a quaternion $q$ can be written in a symplectic form as $q=x+\mathbf{i}y$ with $x,y \in \mathbb{C}$. I read in a couple of engineering references that $x$ is called the simplex-part whereas $y$ is called the perplex-part of the quaternion. Is this widely accepted and if not what is the proper onomatologyin the math community? On the same topic is there a standard name for the two Quaternion parts comprising an Octonion? |
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Cayley-Dickson form of a QuaternionIt is known that using the Cayley-Dickson construction a quaternion $q$ can be written in a symplectic form as $q=x+\mathbf{i}y$ with $x,y \in \mathbb{C}$. I read in a couple of engineering references that $x$ is called the simplex-part whereas $y$ is called the perplex-part of the quaternion. Is this widely accepted and if not what is the proper onomatology in the math community? On the same topic is there a standard name for the two Quaternion parts comprising an Octonion?
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