plus - Plus +
minus - Minus -
mldivide or mrdivide - Left or right matrix divide \ /
mtimes - Matrix multiply *
mpower - Matrix power i.e. exponentiation ^
and these operators can also be used with scalars, which are
regarded as 
matrices, as has been indicated above. The order
of evaluation is brackets, followed by exponentiation, then * or /
and finally + or -, i.e. as normal. Thus we find
>> 2-(2^3-8/4)*3
ans =
-16
The operators 
and / have special meaning when used with matrices.
In particular
>> a=[2 0; 0 2]
a =
2 0
0 2
>> b=[1;1]
b =
1
1
>> x=a\b
x =
0.5000
0.5000
>>
i.e. the MATLAB form x=a b gives the
same result as 
,
but more efficiently, since Gaussian elimination is used. However, the
following also works:
>> x=inv(a)*b
x =
0.5000
0.5000
>>
Although MATLAB was originally designed for matrix manipulations, it
is often useful to be able to perform element by element multiplication,
division or exponentiation.
There are three special operators that allow this, namely
.* which is the times operator, ./ which is the right array divide
and .^ which is the array power operator.
They are used in the following way:
vec4=vec1.*vec2: vec4(i)=vec1(i)*vec2(i), i=1,2,...,n
vec5=vec1./vec2: vec5(i)=vec1(i)/vec2(i), i=1,2,...,n
vec5=vec1.^2: vec5(i)=vec1(i)^2, i=1,2,...,n Here are some examples:
>> x=[-pi 0 pi]
x =
-3.1416 0 3.1416
>> x.^2
ans =
9.8696 0 9.8696
>> y = x .* cos(x)
y =
3.1416 0 -3.1416
>> z = (1+sin(x)) ./ cos(x)
z =
-1.0000 1.0000 -1.0000
Study these examples carefully, as the three operators are very
useful when working with vectors.