Chapter 10 creating and manipulating matrices, Definitions, Chapter 10 – HP 50g Graphing Calculator User Manual
Page 302: Creating and manipulating matrices ,10-1, Definitions ,10-1, Chapter 10 ! creating and manipulating matrices
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:
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
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
.
.
]
[
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
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
=
1
0
0
0
1
0
0
0
1
I
⎩
⎨
⎧
≠
=
=
j
i
if
j
i
if
ij
,
0
,
1
δ