Operations on vectors | Multiplication

Vector multiplication

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 * 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 * More generally, a Lie bracket in a Lie algebra. * Hadamard product – entrywise product of vectors, where . * Outer product - where with results in a matrix. * Triple products – products involving three vectors. * Multiple cross products – products involving more than three vectors. (Wikipedia).

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Vector cross product

The vector cross-product is another form of vector multiplication and results in another vector. In this tutorial I show you a simple way of calculating the cross product of two vectors.

From playlist Introducing linear algebra

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From playlist Linear Algebra for Computer Scientists

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From playlist Basics: Vectors

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Dot product of two vectors

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From playlist Introducing linear algebra

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From playlist Linear Algebra

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From playlist Part 1 Linear Algebra: An In-Depth Introduction with a Focus on Applications

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Matrix multiplication

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From playlist Introducing linear algebra

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From playlist A first course in Linear Algebra - N J Wildberger

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Motivation for the definition of matrix multiplication. Alternative ways of thinking about matrix multiplication.

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Related pages

Dot product | Scalar multiplication | Mathematics | Matrix multiplication | Vector addition | Algebra over a field | Euclidean vector | Triple product | Lie algebra | Hadamard product (matrices) | Outer product | Scalar (mathematics) | Cross product