Search results
Results from the WOW.Com Content Network
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.
This allows recognition from very few labeled examples – in the limit, just one. Neuroscience suggests that natural functionals for a neuron to compute is a high-dimensional dot product between an "image patch" and another image patch (called template) which is stored in terms of synaptic weights (synapses per neuron).
A dot product representation of a simple graph is a method of representing a graph using vector spaces and the dot product from linear algebra. Every graph has a dot ...
Also, the vertical symmetry of f is the reason and are identical in this example. In signal processing, cross-correlation is a measure of similarity of two series as a function of the displacement of one relative to the other. This is also known as a sliding dot product or sliding inner-product. It is commonly used for searching a long signal ...
where the operator denotes a dot product, ^ is the unit vector in the direction of , ‖ ‖ is the length of , and is the angle between and . [ 1 ] The term scalar component refers sometimes to scalar projection, as, in Cartesian coordinates , the components of a vector are the scalar projections in the directions of the coordinate axes .
The dot product of two vectors tangent to the sphere sitting inside 3-dimensional Euclidean space contains information about the lengths and angle between the vectors. The dot products on every tangent plane , packaged together into one mathematical object, are a Riemannian metric.
Get AOL Mail for FREE! Manage your email like never before with travel, photo & document views. Personalize your inbox with themes & tabs. You've Got Mail!
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.