what does "^" and ".^" difference ?

surely "^" and ".^" had difference in their using. but what exactly they does?

Answer 1

[Walter Roberson]

>> [1 2;3 4]^2
ans =
     7    10
    15    22
>> [1 2;3 4].^2
ans =
     1     4
     9    16
>> [1 2; 3 4]*[1 2; 3 4]  %same as ^2
ans =
     7    10
    15    22
>> [1 2; 3 4].*[1 2;3 4]  %same as .^2
ans =
     1     4
     9    16

The formal names of the operations are mpower (^) and power (.^) . ^ is for matrix multiplication repeated, where .^ is for element-by-element multiplication repeatedly.

Answer 2

[Cam]

The dot is a element wise operator, this means that each element is operated on by the element of the same index when you use this. The other "^" will raise any value (scalar, or matrix) to the power of it. A bit difficult to explain in words here is an example:

a = [1 2;3 4]
b = [2 2;2 2]

a.^b = [1 4;9 16]

As you can see it went element by element and applied the operator. 1^2, 2^2; 2^3, 2^4

In contrast if you do:

a = [1 2;3 4]
b = [2 2;2 2]

a^b = %ERROR must be a scalar
a^2 = [1 4;9 16]

The dot is more applicable to other operators like multiplication and division its less used but still often needed as matlab always assumes matricies are being used first.