Quaternion Algebra |
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Editor:
| Surhone, Lambert M. Timpledon, Miriam T. Marseken, Susan F. |
ISBN: | 978-613-0-34367-5 |
Publication Date: | Jun 2010 |
Publisher: | AV Akademikerverlag GmbH & Co. KG
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Book Format: | Paperback |
List Price: | USD $47.00 |
Book Description:
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, a quaternion algebra over a field F is a central simple algebra A over F[1][2] that has dimension 4 over F. Every quaternion algebra becomes the matrix algebra by extending scalars (=tensoring with a field extension), i.e. for a suitable field extension K of F, A otimes_F K is isomorphic to the 2 2 matrix algebra over K. The notion of a...
More DescriptionPlease note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, a quaternion algebra over a field F is a central simple algebra A over F[1][2] that has dimension 4 over F. Every quaternion algebra becomes the matrix algebra by extending scalars (=tensoring with a field extension), i.e. for a suitable field extension K of F, A otimes_F K is isomorphic to the 2 2 matrix algebra over K. The notion of a quaternion algebra can be seen as a generalization of the Hamilton quaternions to an arbitrary base field. The Hamilton quaternions are a quaternion algebra (in the above sense) over F = mathbb{{R}} (the real number field), and indeed the only one over R apart from the 2 2 real matrix algebra, up to isomorphism.