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Let G be a graph with vertex set V. Let F be a field, and f a function from V to F k such that xy is an edge of G if and only if f(x)·f(y) ≥ t. This is the dot product representation of G. The number t is called the dot product threshold, and the smallest possible value of k is called the dot product dimension. [1]
In mathematics, the dot product or scalar product [note 1] is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors), and returns a single number. In Euclidean geometry, the dot product of the Cartesian coordinates of two vectors is widely used.
Desmos was founded by Eli Luberoff, a math and physics double major from Yale University, [3] and was launched as a startup at TechCrunch's Disrupt New York conference in 2011. [4] As of September 2012 [update] , it had received around 1 million US dollars of funding from Kapor Capital , Learn Capital, Kindler Capital, Elm Street Ventures and ...
The scalar projection is defined as [2] = ‖ ‖ = ^ where the operator ⋅ denotes a dot product, ‖a‖ is the length of a, and θ is the angle between a and b. The scalar projection is equal in absolute value to the length of the vector projection, with a minus sign if the direction of the projection is opposite to the direction of b ...
LiveMath is a computer algebra system available on a number of platforms including Mac OS, macOS (), Microsoft Windows, Linux (x86) and Solaris (SPARC). It is the latest release of a system that originally emerged as Theorist for the "classic" Mac in 1989, became MathView and MathPlus in 1997 after it was sold to Waterloo Maple, [1] and finally LiveMath after it was purchased by members of its ...
Also, the dot, cross, and dyadic products can all be expressed in matrix form. Dyadic expressions may closely resemble the matrix equivalents. The dot product of a dyadic with a vector gives another vector, and taking the dot product of this result gives a scalar derived from the dyadic.
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