Abstract |
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We have generalized the three dimensional space to seven dimensional one by using octonions and their multiplication rules. The identity n(n-1)(n-3)(n-7) = 0 have been verified to show that there exist only n = 0, 1, 3 and 7 dimensions for vector spaces. It is shown that three dimensional vector space may be extended to seven dimensional space by means of octonions under certain permutations of combinations of structure constant associated with the octonion multiplication rules.
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Keywords and phrases
three dimensional space, seven dimensional space, octonions, gradient, divergence, curl.
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