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36
Portfolio Frontier of Many Assets
When there are more than two assets, it is extremely tedious to derive and express the portfolio possibility
curve by the methods described above. It is much more convenient to use linear algebra to do this. It requires
only a minimum amount of linear algebra.
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Definition: Column vector, row vector, and matrix
3×1 column vector
1×4 row vector
2×3 matrix
Definition. Transpose of a matrix
Transpose of a 3×1 column vector
a
is a 1×3 row vector and denoted by a
N
:
Transpose of the 2×3 matrix
C
is a 3×2 matrix
Definition: Multiplication of matrices. Let matrices
A
and
B
are defined as
Then, the multiplication
AB
is defined as a 2×2 matrix
Note that the number of columns of
A
must be the same as the number of rows of
B
for proper multiplication
(conformable for multiplication).
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Definition. An
inverse
of a nonsingular square matrix
V
, denoted by
, is a matrix such that
, where
I
is an identity matrix whose diagonal elements are 1 and offdiagonal elements are
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 Fall '08
 Staff

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