Real Projective Space

This article will begin with the claim that Hamilton spent a great deal of time trying to figure out the three-dimensional complex numbers. He was never able to accomplish that. Complex numbers are in the form a+bi where ‘a’ is a real part and ‘bi’ an imaginary with ð ‘–= √−1 The motive behind the claim is that both ð ‘–2 and ð ‘—2= −1; The failure may also have been caused by the lack of a proper definition for the field of complex numbers. To address this issue, the author of this article offers his own definition of the field of complex numbers with key vectots i,j,k taking values (-1,0,1) respectively Of course the field of complex numbers remains unchanged with ð ‘‹ ⃗⃗⃗ =ð ‘¥+𠑦𠑖+𠑧𠑗 under transformation becoming ð ‘‹ ⃗⃗⃗ =𠑥𠑖+𠑦𠑗+𠑧𠑘 vector but it has it’s correspondence in the field of real numbers and it’s a vector (-1,0,1) The entire process of transition between fields, in author’s opinion, is possible thanks to the matrix of transformation It’s form has already been explored earlier on by the same author in his ‘Ternary Mathematics and 3D Placement of Logical Elements Justification’. Professor Juan Weisz (Doctor of Philosophy, Northeastern University, Argentina) generously proposed the concept of field transition, which allows for conversion between imaginary and real numbers without altering the field’s structure or the relationships between its constituent parts. In essense it should work for all entries just the same way it works for the entries of real numbers The fact that serves as the proof is in ð ´â€²ð ´=1 and it works well for both Real and Imaginary number fields which is what we are aiming to prove.