Description

MATRICES
Numerical Methods Applied to Mechatronics
Dr. Jorge A. Olórtegui Yume, Ph.D.
Mechatronics Engineering School
National University of Trujillo
Matrices Dr. Jorge A. Olortegui Yume, Ph.D. 2
OVERVIEW
ã MATRIX : Rectangular array of elements
represented by a single symbol (Ex.: [A]).
ã ELEMENT: Individual entry of a matrix (Ex.: a
23
)
Matrices Dr. Jorge A. Olortegui Yume, Ph.D. 3
OVERVIEW (cont´d)
ã Row: A horizontal set of elements
ã Column: Vertical set of elements.
ã The first subscrip

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MATRICES
Numerical Methods Applied to MechatronicsDr. Jorge A. OlórteguiYume, Ph.D.
MechatronicsEngineeringSchoolNationalUniversityof Trujillo
Matrices
Dr. Jorge A. OlorteguiYume Ph.D.
2
OVERVIEW
ã
MATRIX :
Rectangulararray of elements represented by a single symbol (Ex.: [
A
]).
ã
ELEMENT:
Individualentry of a matrix(Ex.:
a
23
)
Matrices
Dr. Jorge A. OlorteguiYume Ph.D.
3
OVERVIEW (cont´d)
ã
Row:
A horizontal set of elements
ã
Column:
Verticalset of elements.
ã
The first subscript of an element indicates the row while the second indicates the column.
ã
Matrix Size:
m
by
n
(or
m
x
n
).
ã
1 x
n
matrices are
row vectors
.
ã
m
x 1 matrices are
column vectors.
(Ex.:
a
23
)
131211
aaa
312111
aaa
Matrices
Dr. Jorge A. OlorteguiYume Ph.D.
4
SPECIAL MATRICES
ã
Matrices where
m
=
n
are called
square matrices
.
ã
There are a number of special forms of square matrices:
Symmetric
A
5 1 21 3 72 7 8
Diagonal
A
a
11
a
22
a
33
Identity
A
111
Upper Triangular
A
a
11
a
12
a
13
a
22
a
23
a
33
Lower Triangular
A
a
11
a
21
a
22
a
31
a
32
a
33
Banded
A
a
11
a
12
a
21
a
22
a
23
a
32
a
33
a
34
a
43
a
44

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