Page 10-1
Chapter 10
Creating and manipulating matrices
This chapter shows a number of examples aimed at creating matrices in the
calculator and demonstrating manipulation of matrix elements.
Definitions
A matrix is simply a rectangular array of objects (e.g., numbers, algebraics)
having a number of rows and columns. A matrix
A
having n rows and m
columns will have, therefore, n
×
m elements. A generic element of the matrix
is represented by the indexed variable a
ij
, corresponding to row i and column
j. With this notation we can write matrix
A
as
A
= [a
ij
]
n
×
m
. The full matrix is
shown next:
.
]
[
2
1
2
22
21
1
12
11
=
=
×
nm
n
n
m
m
m
n
ij
a
a
a
a
a
a
a
a
a
a
L
O
M
M
L
L
A
A matrix is square if m = n. The transpose of a matrix is constructed by
swapping rows for columns and vice versa. Thus, the transpose of matrix
A
, is
A
T
= [(a
T
)
ij
]
m
×
n
= [a
ji
]
m
×
n
. The main diagonal of a square matrix is the collection
of elements a
ii
. An identity matrix,
I
n
×
n
, is a square matrix whose main
diagonal elements are all equal to 1, and all off-diagonal elements are zero.
For example, a 3
×
3 identity matrix is written as
=
1
0
0
0
1
0
0
0
1
I
An identity matrix can be written as
I
n
×
n
= [
δ
ij
], where
δ
ij
is a function known
as Kronecker’s delta, and defined as
≠
=
=
j
i
if
j
i
if
ij
,
0
,
1
δ
.
