Dot and Cross products for Complex Numbers

Dot and Cross products for Complex Numbers

Post by Herman Kuu » Wed, 08 Dec 2010 20:48:28

Anyone can point me to good documentation using the "Dot" (.) and "Cross"
(x) products with complex numbers? Using




is extremely limited in content and examples.


1. Dot Product on Complex Numbers

2. Discrepancy between dot product and cross product


I am trying to find the angle between two vectors. This
is going to be between -pi and pi and positive for counterclockwise
Using dot product I seem to get the correct results but I can't
the result for the cross product. Can someone help?
I attach a snippet and some explanation below.
v1 = [0.0023 -0.0439];
v2 = [1 0];
v1_3D = [v1 0];
v2_3D = [v2 0];

CP = cross(v2_3D, v1_3D); % order matters: rotate v2 to v1

sign = 1;
if CP(3) < 0 % clockwise acute angle
sign = -1;

angleDot = sign*acos( dot(v1,v2)/(norm(v1)*norm(v2)) )
angleCross = sign*acos( norm(CP)/(norm(v1_3D)*norm(v2_3D)) )


Now: acos(dot(v1,v2)/(norm(v1)*norm(v2))) -> 1.5185 which seems to be
the correct angle (without the sign)

acos( norm(CP)/(norm(v1_3D)*norm(v2_3D)) ) -> 0.0523, that appear to
pi/2 - 1.5185.

Does anyone know why this happens? I expected them to give the same


3. The dot product and cross product

4. Dot product in the complex space bug ?

5. Solve Cross and Dot product

6. sum products with ANDs

7. Calculating inner products of two complex numbers

8. dot product and vectors with imaginary numbers

9. Dot Product's imaginary component (dot.m)

10. Fastest way to compute dot product (inner product) in Ruby?

11. from image to complex number (complex valued matrix)

12. Table of Contents- dot dot settings for page numbering

13. How to convert numbers using dots into numbers using commas

14. can the product i.d. number be used in place of product key code?

15. Convert numbers to text (from product id # to name of product)