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AntonioLao · **double D algebra -** 03-26-2008, 05:38 PM

Differential domain (DD) as a system of Hadamard matrices can be developed into a robust algebra suitable for describing a background-independence theory, even though a background brane matrix that is infinitely extended can still exist, of Quantized Space-Time (QST) or TQS for Theory of Quantized Spacetime. It satisfies the commutative property of multiplication. However, the resulting products can be set equal to the difference of these matrices wherein the subtrahend is always the same matrix while the minuend is the product of an integer eigenvalue and the one other matrix which for power matrices alternate between odd and even.

Given square symmetric singular Hadamard matrices A and B both of order 2, the matrix multiplication AB=BA. The product is 2B or B-A: AB=BA=2B=B-A. For order 3, AB=3B=2B-A. For order 4, AB=4B=3B-A. For order 5, AB=5B=4B-A. For order 6, AB=6B=5B-A. The general equation for order n is AB=nB=αB-A, where the eigenvalue is α=n-1. The following products and differences give power matrices of A and B. For order 2, A=2A=3A-A, A=4A=5A-A, A=8A=9A-A, A=16A=17A-A. For order 3, A=3A=4A-A, A=9A=10A-A, A=27A=28A-A, A=81A=82A-A. For order 4, A=4A=5A-A, A=16A=17A-A, A=64A=65A-A, A=256A=257A-A. For order 5, A=5A=6A-A, A=25A=26A-A, A=125A=126A-A, A=625A=626A-A. For order 2, B=2A=3A-A, B=4B=5B-A, B=8A=9A-A, B=16B=15B-A. For order 3, B=3A=4A-A, B=9B=8B-A, B=27A=26A-A, B=81B=80B-A. For order 4, B=4A=5A-A, B=16B=15B-A, B=64A=65A-A, B=256B=255B-A. For order 5, B=5A=6A-A, B=25B=24B-A, B=125A=124A-A, B=625B=624B-A.

An electron is the product of BBBBBBBA=BA. On the other hand, an up quark is the product of AAAAAB=AB and the down quark is the product of ABBB=AB. Therefore, a proton is the product of AAAAAAAAAAABBBBB=AB since it is made up of 2 up-quarks and 1 down-quark. The ratio of AB/ BA=n, where n is the order of the Hadamard matrices. For space charges, there are always 2n representing the 2 squares of spacetime energy whose square root is approximately 1832 for n=6 as the ratio of proton mass to electron mass experimental value is approximately 1836.

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AntonioLao Raider of the lost time Status: Offline Posts: 5,613 Thanks Given: 790 Thanked 180x in 174 Posts Join Date: Nov 2003 Rep Power: 80	double D algebra - 03-26-2008, 05:38 PM Differential domain (DD) as a system of Hadamard matrices can be developed into a robust algebra suitable for describing a background-independence theory, even though a background brane matrix that is infinitely extended can still exist, of Quantized Space-Time (QST) or TQS for Theory of Quantized Spacetime. It satisfies the commutative property of multiplication. However, the resulting products can be set equal to the difference of these matrices wherein the subtrahend is always the same matrix while the minuend is the product of an integer eigenvalue and the one other matrix which for power matrices alternate between odd and even. Given square symmetric singular Hadamard matrices A and B both of order 2, the matrix multiplication AB=BA. The product is 2B or B-A: AB=BA=2B=B-A. For order 3, AB=3B=2B-A. For order 4, AB=4B=3B-A. For order 5, AB=5B=4B-A. For order 6, AB=6B=5B-A. The general equation for order n is AB=nB=αB-A, where the eigenvalue is α=n-1. The following products and differences give power matrices of A and B. For order 2, A=2A=3A-A, A=4A=5A-A, A=8A=9A-A, A=16A=17A-A. For order 3, A=3A=4A-A, A=9A=10A-A, A=27A=28A-A, A=81A=82A-A. For order 4, A=4A=5A-A, A=16A=17A-A, A=64A=65A-A, A=256A=257A-A. For order 5, A=5A=6A-A, A=25A=26A-A, A=125A=126A-A, A=625A=626A-A. For order 2, B=2A=3A-A, B=4B=5B-A, B=8A=9A-A, B=16B=15B-A. For order 3, B=3A=4A-A, B=9B=8B-A, B=27A=26A-A, B=81B=80B-A. For order 4, B=4A=5A-A, B=16B=15B-A, B=64A=65A-A, B=256B=255B-A. For order 5, B=5A=6A-A, B=25B=24B-A, B=125A=124A-A, B=625B=624B-A. An electron is the product of BBBBBBBA=BA. On the other hand, an up quark is the product of AAAAAB=AB and the down quark is the product of ABBB=AB. Therefore, a proton is the product of AAAAAAAAAAABBBBB=AB since it is made up of 2 up-quarks and 1 down-quark. The ratio of AB/ BA=n, where n is the order of the Hadamard matrices. For space charges, there are always 2n representing the 2 squares of spacetime energy whose square root is approximately 1832 for n=6 as the ratio of proton mass to electron mass experimental value is approximately 1836. Time independence: [∂E(g)]²=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: ¶a(t)·¶r(t)=c²