Since the update vectors are \Delta x^{(k)} and \Delta x^{(l)}, on p. 273 the \Delta in the boxed equation ought to appear within the parenthesis, i.e. \Delta (x^{(k)})^{T} A ... --> (\Delta x^{(k)})^{T} A ..., as in the slides from Lecture 14.
As currently written, it looks like an A-conjugacy condition on \Delta x^{(l)} and x^{(k)}, not \Delta x^{(k)}.
Since the update vectors are \Delta x^{(k)} and \Delta x^{(l)}, on p. 273 the \Delta in the boxed equation ought to appear within the parenthesis, i.e. \Delta (x^{(k)})^{T} A ... --> (\Delta x^{(k)})^{T} A ..., as in the slides from Lecture 14.
As currently written, it looks like an A-conjugacy condition on \Delta x^{(l)} and x^{(k)}, not \Delta x^{(k)}.