The Nonexistence of Pseudoquaternions in {\mathbb{C}^{2\times 2}} |
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Authors: | Drahoslava Janovská Gerhard Opfer |
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Institution: | (3) Institute Math., Hanoi, Vietnam; |
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Abstract: | The field of quaternions, denoted by
\mathbbH{\mathbb{H}} can be represented as an isomorphic four dimensional subspace of
\mathbbR4×4{\mathbb{R}^{4\times 4}}, the space of real matrices with four rows and columns. In addition to the quaternions there is another four dimensional
subspace in
\mathbbR4×4{\mathbb{R}^{4\times 4}} which is also a field and which has – in connection with the quaternions – many pleasant properties. This field is called
field of pseudoquaternions. It exists in
\mathbbR4×4{\mathbb{R}^{4\times 4}} but not in
\mathbbH{\mathbb{H}}. It allows to write the quaternionic linear term axb in matrix form as Mx where x is the same as the quaternion x only written as a column vector in
\mathbbR4{\mathbb{R}^4}. And M is the product of the matrix associated with the quaternion a with the matrix associated with the pseudoquaternion b. |
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Keywords: | |
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