TonyEsposito said:Hi i have seen in abook the dot product defined as follows:
Dot(A,B)=(1/4)[Norm(A+B)^2-Norm(A-B)^2]
how this definition connect with the common one: Dot(A,B)=Sum(ai*bi)
Thanks!
The strange dot product is a mathematical operation that takes two vectors and produces a scalar value. It differs from the traditional dot product in that it includes an additional term that involves the cross product of the two vectors.
The name "strange" comes from the fact that it deviates from the traditional definition of the dot product. The additional term involving the cross product makes it unique and "strange" compared to the standard dot product.
The strange dot product has applications in physics, particularly in the study of electromagnetic fields and fluid dynamics. It is also used in computer graphics and computer vision for tasks such as object recognition and image processing.
The formula for calculating the strange dot product is: A • B = AxBx + AyBy + AzBz + (AxBy - AyBx) + (AxBz - AzBx) + (AyBz - AzBy). This includes the traditional dot product (A • B = AxBx + AyBy + AzBz) as well as the additional cross product terms.
Some properties of the strange dot product include: distributivity, commutativity, and associativity. It also follows the Cauchy-Schwarz inequality and can be used to calculate the angle between two vectors. However, it is not always positive-definite like the traditional dot product.