Appendix E. Lagrange Multipliers
Lagrange multipliers, also sometimes called undetermined multipliers, are used to
nd the stationary points of a function of several variables subject to one or more
constraints.
Consider the problem of nding the maximum of
From Zero to Reproducing Kernel Hilbert Spaces
in Twelve Pages or Less
Hal Daum III
e
11 February 2004
1
Introduction
Reproducing Kernel Hilbert Spaces (RKHS) have been found incredibly useful in
the machine learning community. Their theory has been aroun
2 SPANNING ORIENTED
SUBSPACES
After many attempts at formalizing space and spatial relationships, the concept of a vector
space emerged as the useful framework for geometrical computations. We use it as our
point of departure, and use some of the standard
CHAPTER I
Vector Spaces
As usual, a collection of objects will be called a set. A member of the
collection is also called an element of the set. It is useful in practice to
use short symbols to denote certain sets. For instance, we denote by R
the set of
Proposition. Let f : R R. Then (regardless of whether f is a Borel function) the set
of discontinuities of f ,
D = cfw_x R : f is discontinuous at x,
is a Borel set.
Proof. Recall that f is continuous at x if > 0 > 0 |y x| < = |f (y) f (x)| <
. This is eq