1.2 MATRIX OPERATIONS
The basic matrix operations are addition(+), subtraction(-), multiplication (*),
and conjugate transpose(‘) of matrices. In addition to the above basic operations,
MATLAB has two forms of matrix division: the left inverse operator \
or the right inverse operator /.
Matrices of the same dimension may be subtracted or added. Thus if E and F
are entered in MATLAB as
E = [7 2 3; 4 3 6; 8 1 5];
F = [1 4 2; 6 7 5; 1 9 1];
and
G = E - F
H = E + F
then, matrices G and H will appear on the screen as
G =
6 -2 1
-2 -4 1
7 -8 4
H =
8 6 5
10 10 11
9 10 6
A scalar (1-by-1 matrix) may be added to or subtracted from a matrix. In this
particular case, the scalar is added to or subtracted from all the elements of another
matrix. For example,
J = H + 1
gives
J =
9 7 6
11 11 12
10 11 7
Matrix multiplication is defined provided the inner dimensions of the two operands
are the same. Thus, if X is an n-by-m matrix and Y is i-by-j matrix


X*Y is defined provided m is equal to i. Since E and F are 3-by-3 matrices,
the product
Q = E*F
results as
Q =
22 69 27
28 91 29
19 84 26
Any matrix can be multiplied by a scalar. For example,
2*Q
gives
ans =
44 138 54
56 182 58
38 168 52
Note that if a variable name and the “=” sign are omitted, a variable name ans
is automatically created.
Matrix division can either be the left division operator \ or the right division
operator /. The right division a/b, for instance, is algebraically equivalent to
a
b
while the left division a\b is algebraically equivalent to
b
a
.
If Z * I = V and Z is non-singular, the left division, Z\V is equivalent to
MATLAB expression
I = inv(Z) *V
where inv is the MATLAB function for obtaining the inverse of a matrix. The
right division denoted by V/Z is equivalent to the MATLAB expression
I = V *inv(Z)
There are MATLAB functions that can be used to produce special matrices.
Examples are given in Table 1.3.