User:CStark10/sandbox

Adding citation for my current Physics class assignment regarding updating Vector multiplication wiki page. Will be adding historical information regarding scaler quantities mathematicians and there footprints on the algebra used regarding physics vectors.

Plans for Vector Multiplication Article:

1) Update existing information with vector arrow symbols on all vector text (using source code) to represent it as a true vector.

2) Add some reference links to existing data

3) Add new data about the history and historical roots of the mathematicians who helped pave the way for the mathematics used within vector multiplication.

Below is the existing text I will edit to add the vectorization of the vector text.

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 magnitudes of the two vectors and the cosine of the angle between the two vectors. Alternatively, it is defined as the product of the projection of the first vector onto the second vector and the magnitude of the second vector. Thus,
 * A ⋅ B = |A| |B| cos θ (CHANGES WILL BE MADE HERE)
 * More generally, a bilinear product in an algebra over a field.
 * Cross product – also known as the "vector product", a binary operation on two vectors that results in another vector. The cross product of two vectors in 3-space is defined as the vector perpendicular to the plane determined by the two vectors whose magnitude is the product of the magnitudes of the two vectors and the sine of the angle between the two vectors. So, if n̂ is the unit vector perpendicular to the plane determined by vectors A and B,
 * A × B = |A| |B| sin θ n̂ (CHANGES WILL BE MADE HERE)
 * More generally, a Lie bracket in a Lie algebra.
 * Hadamard product – entrywise product of vectors, where $$(A \odot B)_i = A_i B_i$$.
 * Outer product - where $$(\mathbf{a} \otimes \mathbf{b})$$ with $$\mathbf{a} \in \mathbb{R}^d, \mathbf{b} \in \mathbb{R}^d$$ results in a $$(d \times d)$$ matrix.