Robin Hankin wrote:
Hello everybody
When one is working with complex matrices, "transpose" very nearly
always means
*Hermitian* transpose, that is, A[i,j] <- Conj(A[j,i]).
One often writes A^* for the Hermitian transpose.
I have only once seen a "real-life" case
where transposition does not occur simultaneously with complex conjugation.
And I'm not 100% sure that that wasn't a mistake.
Matlab and Octave sort of recognize this, as "A'" means the Hermitian
transpose of "A".
In R, this issue makes t(), crossprod(), and tcrossprod() pretty much
useless to me.
OK, so what to do? I have several options:
1. define functions myt(), and mycrossprod() to get round the problem:
myt <- function(x){t(Conj(x))}
2. Try to redefine t.default():
t.default <- function(x){if(is.complex(x)){return(base::t(Conj(x)))}
else {return(base::t(x))}}
(This fails because of infinite recursion, but I don't quite understand
why).
You should call base::t.default, not base::t. Then this will work. The
same solution fixes the one below, though you won't even need the base::
prefix on t.default.
Duncan Murdoch
3. Try to define a t.complex() function:
t.complex <- function(x){t(Conj(x))}
(also fails because of recursion)
4. Try a kludgy workaround:
t.complex <- function(x){t(Re(x)) - 1i*t(Im(x))}
Solution 1 is not good because it's easy to forget to use myt() rather
than t()
and it does not seem to be good OO practice.
As Martin Maechler points out, solution 2 (even if it worked as desired)
would break the code of everyone who writes a myt() function.
Solution 3 fails and solution 4 is kludgy and inefficient.
Does anyone have any better ideas?
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