Search results
Results From The WOW.Com Content Network
NumPy (pronounced / ˈ n ʌ m p aɪ / NUM-py) is a library for the Python programming language, adding support for large, multi-dimensional arrays and matrices, along with a large collection of high-level mathematical functions to operate on these arrays. [3]
In linear algebra, linear transformations can be represented by matrices.If is a linear transformation mapping to and is a column vector with entries, then there exists an matrix , called the transformation matrix of , [1] such that: = Note that has rows and columns, whereas the transformation is from to .
3D visualization of a sphere and a rotation about an Euler axis (^) by an angle of In 3-dimensional space, according to Euler's rotation theorem, any rotation or sequence of rotations of a rigid body or coordinate system about a fixed point is equivalent to a single rotation by a given angle about a fixed axis (called the Euler axis) that runs through the fixed point. [6]
Apache Lucene is a high-performance, open source, full-featured text search engine library written entirely in Java. OpenSearch (software) and Solr: the two most well-known search engine programs (many smaller exist) based on Lucene. Gensim is a Python+NumPy framework for Vector Space modelling.
The state space of the composite system is simply C ( X ) ⊗ C ( Y ) = C ( X × Y ) . {\displaystyle C(X)\otimes C(Y)=C(X\times Y).} A state on the composite system is a positive element ρ of the dual of C( X × Y ), which by the Riesz–Markov theorem corresponds to a regular Borel measure on X × Y .
An open cover of a topological space X is a family of open sets U α such that their union is the whole space, U α = X. The order or ply of an open cover A {\displaystyle {\mathfrak {A}}} = { U α } is the smallest number m (if it exists) for which each point of the space belongs to at most m open sets in the cover: in other words U α 1 ∩ ...
The Standard Template Library overloads its built-in swap function to exchange the contents of containers efficiently this way. [1] As pointer variables are usually of a fixed size (e.g., most desktop computers have pointers 64 bits long), and they are numeric, they can be swapped quickly using XOR swap.
There is an exponential increase in volume associated with adding extra dimensions to a mathematical space.For example, 10 2 = 100 evenly spaced sample points suffice to sample a unit interval (try to visualize a "1-dimensional" cube) with no more than 10 −2 = 0.01 distance between points; an equivalent sampling of a 10-dimensional unit hypercube with a lattice that has a spacing of 10 −2 ...