Optimization Models
EE 127 / EE 227AT
Johannes O. Royset
EECS department
UC Berkeley
Spring 2016
Sp16
1 / 18
LECTURE 4 (Chapter 4, minus 4.4.6)
Symmetric Matrices
Whoever think algebra is a trick in
obtaining unknowns has thought in
vain. No attention sho
Optimization Models
EE 127 / EE 227AT
Johannes O. Royset
EECS department
UC Berkeley
Spring 2016
Sp16
1 / 42
LECTURE 1
Introduction
Because the shape of the whole
universe is most perfect and, in
fact, designed by the wisest
creator, nothing in all of the
EE 127/227AT Spring 2016 Discussion 1
1
Frobenius Norm
The Frobenius norm for a matrix A Rmn is dened as
m
A
F
n
a2
ij
=
i=1 j=1
1. Show that A
2
F
= Tr(AT A).
2. Let A, B Rmn with R(A) R(B). Show that
A+B
2
F
= A
1
2
F
+ B
2
F
2
Ane Sets and Projections
Optimization Models
EE 127 / EE 227AT
Johannes O. Royset
EECS department
UC Berkeley
Spring 2016
Sp16
1 / 36
LECTURE 3 (Chapter 3, minus 3.7)
Matrices and Linear Maps
The Matrix is everywhere. It is all
around us.
Morpheus
Sp16
2 / 36
Outline
1
Introducti
Optimization Models
EE 127 / EE 227AT
Johannes O. Royset
EECS department
UC Berkeley
Spring 2016
Sp16
1 / 27
LECTURE 5 (Chapter 5, minus 5.3.3)
Singular Value Decomposition
The license plate of Gene Golub
(19322007).
Sp16
2 / 27
Outline
1
The singular val
Optimization Models
EE 127 / EE 227AT
Johannes O. Royset
EECS department
UC Berkeley
Spring 2016
Sp16
1 / 46
LECTURE 2 (Chapter 2)
Vectors and Functions
Mathematicians are like
Frenchmen: whatever you say to
them, they translate into their own
language, a