Hadamard adjoints

[AntonioLao]

In the study of linear algebra for matrices and determinants, one involving the transpose of cofactors is called the adjoint of a given matrix A. In some textbooks the adjoint of a matrix A multiplied by A is equal to the product of the determinant of A with the identity matrix. Wherever and whenever the determinant of A is not equal to zero the inverse of A is determined as the adjoint matrix divided by the determinant. This is true for all nonsingular square matrices.

However, for singular symmetric Hadamard matrices their inverses cannot be defined since their determinants vanish. On the other hand, their adjoint matrices can be separately determined for any matrix order. Except for all 2x2 symmetric Hadamard matrices, the adjoint matrices are simply the zero matrices of the same order. The unique property of the adjoints of 2x2 symmetric Hadamard matrices is that the 4 elements are either all +1 or all -1 such that their matrix product with any 2x2 symmetric Hadamard matrix is also the 2x2 zero matrix. Therefore, a general rule can be given that the matrix product of any Hadamard matrix with its adjoint matrix always gives the zero matrix. These 2x2 adjoint matrices of nonzero elements can be used to represent the absolute background of quantum space-time as cubic lattices of squares of energy with vertex signs of (+,+,+,+,+,+,+,+) or (-,-,-,-,-,-,-,-).

[mkirkpatrick]

Look deeply into the matrix what do you see?The thread that links all matrices is
consciousness.




regards michael.

[AntonioLao]

The important thing is that a conscious matrix is time independence or it has no sense of time. It is timeless and eternal.

[mkirkpatrick]

The important thing is that a conscious matrix is time independence or it has no sense of time. It is timeless and eternal.

Yes, thats sounds about right,however,I would add that the conscious matrix is
only time independant when "not expressed in relativity".



regards michael.