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Originally Posted by AntonioLao  continuous vs. discrete symmetry
Hadamard matrices possess continuous symmetry not discrete left-right symmetry of parity operation. When a circle is rotated whether clockwise (CW) or counterclockwise (CCW) by someone when another person is not looking there is no way the person can tell whether it has rotated. This is an example of continuous symmetry. In this sense, Hadamard matrices are represented by two linked circles where and when each undergoes continuous rotations CW or CCW. The mirror image represents a broken discrete symmetry of parity operation. The original is H+ the image is H-. Together they represent basic quanta of spacetime. The smallest matrix that can be used to represent a quantum is a 2 by 2 real elements matrix where the elements are e11=1, e12=-1, e21=-1, and e22=1 for H+. They are e11=-1, e12=1, e21=1, and e22=-1 for H-. The determinants of these 2 by 2 matrices are all zero implying that multiplicative inverse does not exist. |
This is leading somewhere,i just know it!
regards michael.