what is the different between B^2 and B.^2

what is the different between B^2 and B.^2?

[Paolo Volpe]

thank you

Answer 1

[Stephen23]

These are certainly NOT the same operations, and the sizes of the matrices does not determine which operations to use. You need to pick the operation, based on what you are trying to calculate.

From their documentation pages:

• .^ power gives the "element-wise power", so that C = A.^B raises each element of A to the corresponding power in B.
• ^ mpower gives the "matrix power", so that C = A^B computes A to the B power. For your example, with a scalar B, this is equivalent to A*A.

Lets try them: first we can look at the power operation:

>> A = [1,2;3,4];
>> B = 2;
>> A.^2 % element-wise power
ans =
    1    4
    9   16

You can see that each element of the output is simply the element of A to the power 2:

>> A(1,1)*A(1,1)
ans =  1
>> A(1,2)*A(1,2)
ans =  4
>> A(2,1)*A(2,1)
ans =  9
>> A(2,2)*A(2,2)
ans =  16

What about A.^3? I am sure that you can spot the pattern:

>> A.^3
ans =
    1    8
   27   64
>> A(2,2)*A(2,2)*A(2,2)
ans =  64

Now lets look at the mpower operation:

>> A^2
ans =
    7   10
   15   22

And you will see that this is simply equivalent to:

>> A*A
ans =
    7   10
   15   22

Now try A^3 to see the pattern:

>> A^3
ans =
    37    54
    81   118
>> A*A*A
ans =
    37    54
    81   118

Read about the differences between matrix (linear algebra) and array (element-wise) operations here:

https://www.mathworks.com/help/matlab/matlab_prog/array-vs-matrix-operations.html

Answer 2

[Minyoung Hong]

thanks!