“Whoa! It's like Spotify but for academic articles.”

Instant Access to Thousands of Journals for just $40/month

Get 2 Weeks Free

The Nonexistence of Pseudoquaternions in



The field of quaternions, denoted by can be represented as an isomorphic four dimensional subspace of , the space of real matrices with four rows and columns. In addition to the quaternions there is another four dimensional subspace in 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 but not in . 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 . And M is the product of the matrix associated with the quaternion a with the matrix associated with the pseudoquaternion b . Now, the field of quaternions can also be represented as an isomorphic four dimensional subspace of over , the space of complex matrices with two rows and columns. We show that in this space pseudoquaternions with all the properties known from do not exist. However, there is a subset of for which some of the properties are still valid. By means of the Kronecker product we show that there is a matrix in which has the properties of the pseudoquaternionic matrix.



Advances in Applied Clifford AlgebrasSpringer Journals

Published: Sep 1, 2011

DOI: 10.1007/s00006-010-0273-1

Free Preview of First Page

Loading next page...

You're reading a free preview. Subscribe to read the entire article.

And millions more from thousands of peer-reviewed journals, for just $40/month

Get 2 Weeks Free

To be the best researcher, you need access to the best research

  • With DeepDyve, you can stop worrying about how much articles cost, or if it's too much hassle to order — it's all at your fingertips. Your research is important and deserves the top content.
  • Read from thousands of the leading scholarly journals from Springer, Elsevier, Nature, IEEE, Wiley-Blackwell and more.
  • All the latest content is available, no embargo periods.