matlab - What does operator "dot" (.) mean?

Question

Given the code :

 A = [1 2 3; 3 2 1]
 B = A.^2

The output :

B =

     1     4     9
     9     4     1

But if I do this : B = A^2

The output is :

Error using  ^ 
Inputs must be a scalar and a square matrix.
To compute elementwise POWER, use POWER (.^) instead.

What does the operator . do exactly ?

Answer 1

The dot itself is not an operator, .^ is.

The .^ is a pointwise1 (i.e. element-wise) power, as .* is the pointwise product.

.^ Array power. A.^B is the matrix with elements A(i,j) to the B(i,j) power. The sizes of A and B must be the same or be compatible.

C.f.

• "Array vs. Matrix Operations": https://mathworks.com/help/matlab/matlab_prog/array-vs-matrix-operations.html
• "Pointwise": http://en.wikipedia.org/wiki/Pointwise
• "Element-Wise Operations": http://www.glue.umd.edu/afs/glue.umd.edu/system/info/olh/Numerical/Matlab_Matrix_Manipulation_Software/Matrix_Vector_Operations/elementwise

1) Hence the dot.