HP 50g User Manual page 302

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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