Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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2. Vector Notation
In this course we will do a lot of calculations on vectors and matrices. This especially requires
extensive use of the transpose operator. For example, a 3x3 matrix can be denoted equally by their row or
column vectors:
Pi
P2
= ( r} r} r} )" = ( ef & d )
A3×3 =
P3
A rigid transformation on homogenous coordinates in space can be described with the following matrix:
r11
r12
r13
t1
- ( )-
R
t
r22 r23 t2
t3
r21
A =
r31
r32
r33
1
0 0
1
Make yourself familiar with the alternative notations. What is the simplest way to describe the product of this
matrix with a 4-vector v =
(#1, 82, 23, w)" = (x", w)" ?
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Transcribed Image Text:2. Vector Notation In this course we will do a lot of calculations on vectors and matrices. This especially requires extensive use of the transpose operator. For example, a 3x3 matrix can be denoted equally by their row or column vectors: Pi P2 = ( r} r} r} )" = ( ef & d ) A3×3 = P3 A rigid transformation on homogenous coordinates in space can be described with the following matrix: r11 r12 r13 t1 - ( )- R t r22 r23 t2 t3 r21 A = r31 r32 r33 1 0 0 1 Make yourself familiar with the alternative notations. What is the simplest way to describe the product of this matrix with a 4-vector v = (#1, 82, 23, w)" = (x", w)" ?
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