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