Linear associative algebra and quaternions
<p>Let us assume that there exists a system E of distinct elements a<sub>1</sub>, a<sub>2</sub>, a<sub>3</sub>, .......... and that there also exist processes of combinations in a specified order of any two of these elements or of any one with itself, each o...
| Main Author: | |
|---|---|
| Format: | Others |
| Language: | en |
| Published: |
University of Saskatchewan
2011
|
| Online Access: | http://library.usask.ca/theses/available/etd-08042010-092938/ |
| id |
ndltd-USASK-oai-usask.ca-etd-08042010-092938 |
|---|---|
| record_format |
oai_dc |
| spelling |
ndltd-USASK-oai-usask.ca-etd-08042010-0929382013-01-08T16:35:09Z Linear associative algebra and quaternions Stewart, Jean <p>Let us assume that there exists a system E of distinct elements a<sub>1</sub>, a<sub>2</sub>, a<sub>3</sub>, .......... and that there also exist processes of combinations in a specified order of any two of these elements or of any one with itself, each of which yields a determinate result which is also an element of the system E. These processes we shall denote by</p> <p>(1) the 'first direct operation' or as it is commonly called in Algebra 'addition'.</p> <p>(2) the 'second direct operation' or 'multiplication'</p> <p>(3) the 'first inverse operation' or 'subtraction'</p> <p>(4) the 'second inverse operation' or 'division'.</p> <p>Two combinations of elements of the system are said to be equal when either may be substituted for the other in all relations between the elements without destroying any such relation.</p> University of Saskatchewan 2011-08-05 text application/pdf http://library.usask.ca/theses/available/etd-08042010-092938/ http://library.usask.ca/theses/available/etd-08042010-092938/ en unrestricted I hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to University of Saskatchewan or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report. |
| collection |
NDLTD |
| language |
en |
| format |
Others
|
| sources |
NDLTD |
| description |
<p>Let us assume that there exists a system E of distinct elements a<sub>1</sub>, a<sub>2</sub>, a<sub>3</sub>, .......... and that there also exist processes of combinations in a specified order of any two of these elements or of any one with itself, each of which yields a determinate result which is also an element of the system E. These processes we shall denote by</p>
<p>(1) the 'first direct operation' or as it is commonly called in Algebra 'addition'.</p>
<p>(2) the 'second direct operation' or 'multiplication'</p>
<p>(3) the 'first inverse operation' or 'subtraction'</p>
<p>(4) the 'second inverse operation' or 'division'.</p>
<p>Two combinations of elements of the system are said to be equal when either may be substituted for the other in all relations between the elements without destroying any such relation.</p> |
| author |
Stewart, Jean |
| spellingShingle |
Stewart, Jean Linear associative algebra and quaternions |
| author_facet |
Stewart, Jean |
| author_sort |
Stewart, Jean |
| title |
Linear associative algebra and quaternions |
| title_short |
Linear associative algebra and quaternions |
| title_full |
Linear associative algebra and quaternions |
| title_fullStr |
Linear associative algebra and quaternions |
| title_full_unstemmed |
Linear associative algebra and quaternions |
| title_sort |
linear associative algebra and quaternions |
| publisher |
University of Saskatchewan |
| publishDate |
2011 |
| url |
http://library.usask.ca/theses/available/etd-08042010-092938/ |
| work_keys_str_mv |
AT stewartjean linearassociativealgebraandquaternions |
| _version_ |
1716532868904124416 |