Page 33 - Numerical Analysis Using MATLAB and Excel

Chapter 1 Introduction to MATLAB

6
11
We will now define Matrix Multiplication and Element−by−Element multiplication.

1. Matrix Multiplication (multiplication of row by column vectors)

Let
A = [ a a a … a ] 1 2 3 n
and
B = [ b b b … b ] 1 2 3 n '

be two vectors. We observe that is defined as a row vector whereas is defined as a column
B
A
vector, as indicated by the transpose operator (′). Here, multiplication of the row vector by
A
the column vector B , is performed with the matrix multiplication operator (*). Then,

A*B = [ a b + a b + a b + … + a b ] n n = sin gle value (B.15)
3
2
1
2
1
3
For example, if
A = [ 1 2 3 4 5 ]
and
]
–
B = – [ 2 6 3 8 7 '
the matrix multiplication A*B produces the single value 68, that is,
)
A∗ B = 1 × – ( 2 + 2 × 6 + 3 × – ( 3 + 4 × 8 + 5 × 7 = 68
)
and this is verified with the MATLAB script

A=[1 2 3 4 5]; B=[ −2 6 −3 8 7]'; A*B % Observe transpose operator (‘) in B
ans =

68
Now, let us suppose that both and are row vectors, and we attempt to perform a row−by−
B
A
row multiplication with the following MATLAB statements.
A=[1 2 3 4 5]; B=[−2 6 −3 8 7]; A*B % No transpose operator (‘) here
When these statements are executed, MATLAB displays the following message:
??? Error using ==> *

Inner matrix dimensions must agree.
Here, because we have used the matrix multiplication operator (*) in A*B, MATLAB expects

1−20 Numerical Analysis Using MATLAB® and Excel®, Third Edition
Copyright © Orchard Publications