If w, z Cn, define their (Hermitian) dot product by w z = _n j=1 wj zj . a. Check that the following properties hold: (i) w z = z w for all w, z Cn. (ii) (cw) z = c(w z) for all w, z Cn and scalars c. (iii) (v + w) z = (v z) + (w z) for all v,w, z Cn. (iv) z z 0 for all z Cn and z z = 0 only if z = 0. b. Defining the length of a vector z Cn by _z_ = z z, prove the triangle inequality for vectors in Cn: _w + z_ _w_ + _z_ for all w, z Cn.

L16 - 4 Higher Derivatives If y = f (x)s iiilwenﬁndidi,a ▯▯ new function called f (x). The limit deﬁnition: ▯▯ ▯▯▯ In the...