A right handed coordinate system can be converted
to a left handed coordination system (or via versa) by
Inverting any one coordinate basis (such as
replacing z with -z)
or swapping any two coordinate
basis (such as x and y).
However I'm not sure
you can change a matrix which does some function in a right hand
coordinate system to make it do a similar function in a left hand
system in the way you suggest.
the top row in the matrix is associated with 'x' dimension and
the left column is also associated with 'x' dimension so we need
to swap both rows and columns and I suspect other things may also
need to be changed. So I think the change to the matrix may be
If you want convert Euler angle to a matrix using
left hand coodrinate system you should be able to derive the
matrix using the standard you want to use in a similar way that
the right hand matrix is derived on this
this involves is working out the matrix for yaw, pitch and roll
individually using left hand coordinate. Then multiply these
individual matrices in the order appropriate for the type of
euler angles you want to use (yaw, pitch, roll).
If you want to convert a matrix that
does a function in right-handed space to do the same function in
left-handed space, you need to invert both z-column and z-row
(which implies that the  element is unchanged).
up the "similarity transform"
= matrix_into_space * function * matrix_from_space
> If you want to convert a matrix that
does a function in right-handed space to do the same function
> left-handed space, you need to invert both
z-column and z-row (which implies that the  element
If we are converting from
right->left by inverting the z coordinate, then I think
that in addition to inverting both z-column and z-row I suspect
we also need to invert any z-terms in the body of the matrix.
Would you agree with this? In this case, since we are talking
about euler angle to matrix, then I suggest this means we also
invert attitude (rotate about z)?