Reg:

[snip]
Peter, the stage is now set to introduce Eigenvectors,
Eigenvalues and Sylvesters theorem for square matrices.
;o)
---
Reg
[snip]

Ahhhh... Sylvester, I knew him well!

Roy even fusses at me and insists that the transformation matrix M between
v, i and a, b include a factor of 1/2 as:

a = v/2 + Ri/2 = 1/2 [v + Ri]
b = v/2 - Ri/2 = 1/2 [v - Ri]

i.e. M is:

|1/2 R/2|
|1/2 -R/2|

so that the M is chosen for the voltage and current values to match the
values of v and i found
in solutions of the Telegraphists Equation.

That's fine, but with that simple multiplier common to all elements of the
linear combination of electricals to make the waves, it just don't matter
since as you know, when you form rho = b/a the factor of 1/2 just drops out.

I suppose introducing the "outer product" of the two vectors B = [b1, b2]
and [A^-1]'[ = [1/a1, 1/a2]'
as Bx[A^-1]' = S to form the two by two Scattering Matrix and showing that
the factor of 1/2 disappears there as well would be far far too much for
this group to assimilate!

I can hear Oliver rolling over in his grave!

Long live Sylvester!

;-)

--
Peter K1PO
Indialantic By-the-Sea, FL.