# Definitions; Chapter 10 - Creating And Manipulating Matrices , - HP 48gII User Manual

Graphing calculator.

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
j. With this notation we can write matrix A as A = [a
shown next:
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
T
= [(a
)
]
= [a
]
. The main diagonal of a square matrix is the collection
×
×
ij
m
n
ji
m
n
. An identity matrix, I
of elements a
ii
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
as Kronecker's delta, and defined as
, corresponding to row i and column
ij
a
a
11
12
a
a
21
22
[
a
]
ij
n
×
m
M
M
a
a
n
1
n
2
, is a square matrix whose main
×
n
n
1
0
0
I
=
0
1
0
0
0
1
], where δ
= [δ
×
n
n
ij
, 1
if
i
j
δ
ij
, 0
if
i
]
. The full matrix is
×
ij
n
m
L
a
1
m
L
a
2
m
.
O
L
a
nm
is a function known
ij
.
j
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