# HP 50g User Manual Page 302

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