From Osher Doctorow
The initial or near-initial Universe is usually considered to have
been "unified" with respect to fundamental forces, and arguably with
respect to everything else. This suggests a scalar rather than
tensor or matrix representation at that time.
The scalar has closeness if not isomorphism to diagonal matrices
(e.g., with constant diagonal), and the change of phase corresponds to
some nonzero off-diagonal elements, which extends in different
coordinate systems to matrix representations of tensors. The
diagonal afterward still retains its +/- phase characterstic because:
1) Trace(A) = sum aii (sum of diagonal elements) = sum(lambda_i) (sum
of eigenvalues of A)
The other key invariant, the determinant, begins the multiplication-
division phase, for example in a 2x2 matrix with:
2) det(A) = a11a22 - a12a21
where A is the matrix with elements aij, i and j subscripts (i, j = 1,
2)
As dimensions increase, (3) involves more alternating sums but also
more factors in each term, while (1) remains of exactly the same form
except the numbers of terms added increases.
Osher Doctorow
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