Bare minimum on matrix algebra
Psychology 588: Covariance structure and factor models
Jan 22, 2010

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Matrix multiplication
2
•
Consider three notations for linear combinations
1
1
2
2
,
1,
, ,
1,
,
,
1,
,
ij
i
j
i
j
ip
jp
j
j
y
x b
x b
x b
i
n
j
m
j
m
=
+
+
+
=
=
=
=
=
y
Xb
Y
XB
"
…
…
…
•
Matrix multiplication is a very efficient way of writing
simultaneous equation systems (i.e., linear combinations)
11
1
11
1
11
1
1
1
1
m
p
m
n
nm
n
np
p
pm
y
y
x
x
b
b
y
y
x
x
b
b
⎡
⎤ ⎡
⎤
⎡
⎤
⎢
⎥ ⎢
⎥
⎢
⎥
=
⎢
⎥ ⎢
⎥
⎢
⎥
⎢
⎥ ⎢
⎥
⎢
⎥
⎣
⎦
⎣
⎦ ⎣
⎦
"
"
"
#
%
#
#
%
#
#
%
#
"
"
"