The discussion centers on the definition of the dot product, specifically the formula Dot(A,B)=(1/4)[Norm(A+B)^2-Norm(A-B)^2]. This definition is linked to the common dot product formula Dot(A,B)=Sum(ai*bi) through the use of the polarization identity. The connection is established by recognizing that the Norm() function refers to the Euclidean magnitude of a vector, which is essential for deriving the standard dot product formula. The conversation highlights the mathematical relationship between different representations of the dot product.
PREREQUISITESStudents of mathematics, educators teaching linear algebra, and professionals in fields requiring vector analysis will benefit from this discussion.
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!