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.
_______________________________________________________
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).
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
37
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
zeros:
Matrix V must be a square nonsingular matrix.
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '08
 Staff
 Linear Algebra, Column vector, expected utility, N Risky Assets

Click to edit the document details