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:

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.

A

and

B

must have the same size, unless one of them is a scalar.

C.f.

"Matrix and array arithmetic": http://www.mathworks.de/help/techdoc/ref/arithmeticoperators.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.