Due Fri, Sept 25, 2009, 12 Noon
Your Name: (replace this with your name)
September 22, 2009
Instructions: Edit this LaTex ﬁle by inserting your solutions after each problem statement.
Generate a PDF ﬁle from it and e-mail the PDF to the usual class gmail address. You should
not just answer the questions but also give evidence or even proof. You can discuss the homework
with each other in general terms, but not with previous years’ students of Stat 541. Also, you
must write your own solutions and not copy from anyone.
1. Interpretations of matrix multiplication: Assume
X
is of size
n
×
p
and
B
of size
p
×
q
.
(a) If
X
= (
x
1
,
x
2
,...,
x
p
),
B
= (
b
1
,
b
2
,...,
b
p
)
T
, express
XB
=
X
j
=1
,...,p
x
j
b
T
j
A:
(b) If
X
= (
x
1
,
x
2
,...,
x
n
)
T
,
B
= (
b
1
,
b
2
,...,
b
q
), express
(
XB
)
i,k
=
x
T
i
b
k
A:
2. Write the Euclidean inner product as
h
x
,
y
i
=
x
T
y
and the Euclidean squared norm as
k
x
k
2
=
x
T
x
. What is the interpretation of
y
7→
h
y
,
x
i
k
x
k
2
x
?
A: