HP 50G, Руководство пользователя

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Page 10-1
Chapter 10
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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