I'm trying to show that if A is a positive def. matrix with entries in R that the norm ||x|| = (x^tAx)^1/2. I cannot figure out the triangle inequality for this. Is the author correct. What I have underlined I do not understand.

i know that for the dot product you can u*v = u^t * v = v^t u = vu, but how is the author combining x^tVy and y^tVx?

Thanks.