What does operator “dot” (.) mean?

The dot itself is not an operator, .^ is. The .^ is a pointwise┬╣ (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”: …

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What is the operator `.*` doing in matlab?

It does element-by-element multiplication. Quoting Matlab help (or see online help): .* Array multiply.X.*Y denotes element-by-element multiplication. X and Y must have the same dimensions unless one is a scalar. A scalar can be multiplied into anything. For more information see @am304’s link above.