## dot product for complex vector

Asked by Charles Nguyen

### Charles Nguyen (view profile)

on 16 Jun 2019
Latest activity Answered by John D'Errico

### John D'Errico (view profile)

on 16 Jun 2019
Accepted Answer by John D'Errico

### John D'Errico (view profile)

Hello,
In the Matlab example, you have the dot product of the following two vectors A and B and its answer is vector C.
A = [1+i 1-i -1+i -1-i];
B = [3-4i 6-2i 1+2i 4+3i];
Calculate the dot product of A and B.
C = dot(A,B)
C = 1.0000 - 5.0000i
However, when I calculate it, I have vector C = 7 - 17i
That is, I have C vector results as follows below
(1+i) * (3-4i) + (1-i) * (6-2i) + (-1+i) * (1+2i) + (-1-i) * (4+3i) =
(7-i) +( 4-8i) + (-3-i) + (-1-7i) =
7 - 17i.
Hence, could you please tell me how the Matlab got the results (or show me manually how Matlab got the dot product answer) as I have different results than Matlab calculated using dot product?
Thank you,
Charles

### Release

R2018b ### John D'Errico (view profile)

Answer by John D'Errico

### John D'Errico (view profile)

on 16 Jun 2019

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.