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On the 16th of October 1843, Sir William R. Hamilton made the discovery of the quaternion algebra H = qo + qli + q2j + q3k whereby the product is determined by the defining relations ·2 ·2 1 Z =] = - , ij = -ji = k. In fact he was inspired by the beautiful geometric model of the complex numbers in which rotations are represented by simple multiplications z ----t az. His goal was to obtain an algebra...
There are not so many deep results about zero points of monogenic functions, due to the fact that there are too many things that can happen: zeroes are not isolated, zero sets are not disjoint (e.g. zero curves may cross each other). However, the Jacobian matrix of the monogenic function controls how large the zero sets will be, at least if its rank is constant; for example, if the Jacobian is an...
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