help dot

dot Vector dot product.

C = dot(A,B) returns the scalar product of the vectors A and B.

A and B must be vectors of the same length. When A and B are both

column vectors, dot(A,B) is the same as A'*B.

dot(A,B), for N-D arrays A and B, returns the scalar product

along the first non-singleton dimension of A and B. A and B must

have the same size.

So what are A and B?

A = [1+i 1-i -1+i -1-i];

B = [3-4i 6-2i 1+2i 4+3i];

They are row vectors, complex row vectors. So MATLAB forms the result as:

dot(A,B)

ans =

1 - 5i

sum(conj(A).*B)

ans =

1 - 5i

That is, when A and B are both vectors, MATLAB treats them the same as if A and B were column vectors. It effectively thinks of them as both column vectors. Then it forms the result by conjugating A, takes an element-wise product, then sums those terms.

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