If infinity is a square matrix then its determinant is the sum of its infinite cofactors. If these can be reduced to 2 by 2 matrices then 2 basic forms emerged. These are the fundamental Hadamard matrices of 2nd order: H+ and H-. For 3 by 3, these are the 3rd order matrices: H+ and H- so on and so forth. Moreover, these matrices form an algebra with simple rules for matrix addition and multiplication. These are binary operations which operate exclusively for matrices of the same order; all 2x2’s or all 3x3’s never 2x2 and 3x3. The product of H+ and H- gives H-. The product of H+ and H+ gives H+. The product of H- and H- gives H+. The sum of H+ and H- is the zero matrix. H- plus H- gives 2H- and H+ plus H+ gives 2H+.


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