Summary: 1. More on differentiability, differentials and linear approximation.
Let m and n be positive integers.
2. Standard basis vectors.
Definition 2.1. For each j {1, . . . , n} let
ej
be the vector in Rn
all of whose components are zero except the j-th which is one.
Thus if
x = (x1, . . . , xn) Rn
then
x =
n
j=1
xjej.
3. Linear functions.
Definition 3.1. We say
L : Rn
Rm
is linear if whenever c R and x, y Rn
we have

Source: Allard, William K. - Department of Mathematics, Duke University

Collections: Mathematics