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In mathematics, vector multiplication may refer to one of several operations between two (or more) vectors. It may concern any of the following articles: Dot product – also known as the "scalar product", a binary operation that takes two vectors and returns a scalar quantity. The dot product of two vectors can be defined as the product of the ...
Multiplication of a scalar and a vector was accomplished with the same single multiplication operator; multiplication of two vectors of quaternions used this same operation as did multiplication of a quaternion and a vector or of two quaternions.
There are at least two ways of representing quaternions as matrices in such a way that quaternion addition and multiplication correspond to matrix addition and matrix multiplication. One is to use 2 × 2 complex matrices, and the other is to use 4 × 4 real matrices. In each case, the representation given is one of a family of linearly related ...
He then carved the basic rules for multiplication into the bridge: i 2 = j 2 = k 2 = ijk = −1. Hamilton called a quadruple with these rules of multiplication a quaternion, and he devoted the remainder of his life to studying and teaching them. From 1844 to 1850 Philosophical Magazine communicated Hamilton's exposition of quaternions. [2]
We can express quaternion multiplication in the modern language of vector cross and dot products (which were actually inspired by the quaternions in the first place [14]). When multiplying the vector/imaginary parts, in place of the rules i 2 = j 2 = k 2 = ijk = −1 we have the quaternion multiplication rule:
WASHINGTON (Reuters) -The Trump transition team is considering a former Uber executive and three current or former Republican congressmen - one of whom is now a Fox News host - to lead the U.S ...
Plus, even though you’re walking faster, you’re likely still in zone 2 anyway. Ultimately, weight loss is tricky—and determined by a lot more than your exercise selection. For example, ...
2. Ohio State (9-1) The Buckeyes started a little slowly against Northwestern but stepped on the gas late in the first half, scoring three times in the final seven minutes of the second quarter to ...
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