The Mathematics of Financial Modelingand Investment Management

5-Matrix Algebra Page 144 Wednesday, February 4, 2004 12:49 PM

144 The Mathematics of Financial Modeling and Investment Management

EXHIBIT 5.1 Graphical Representation of Vectors

Matrices

An n××××m matrix is a bidimensional ordered array of n×m numbers.

Matrices are usually indicated with bold-face upper case letters. Thus,

the generic matrix A is an n×m array of the form

a 11 , ·a 1 ,j· a 1 ,m

· ··· ·

A = ai, 1 ·aij, ·aim,

· ··· ·

an, 1 ·anj, · anm,

Note that the first subscript indicates rows while the second sub-

script indicates columns. The entries aij—called the elements of the

matrix A—are the numbers at the crossing of the i-th row and the j-th

column. The commas between the subscripts of the matrix entries are

omitted when there is no risk of confusion: aij, ≡aij. A matrix A is often

indicated by its generic element between brackets:

A = {}aij nm or A = []aijnm