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GNU Octave also allows vectorization and half-vectorization with vec(A) and vech(A) respectively. Julia has the vec(A) function as well. In Python NumPy arrays implement the flatten method, [ note 1 ] while in R the desired effect can be achieved via the c() or as.vector() functions or, more efficiently, by removing the dimensions attribute of ...
In mathematics, the Kronecker product, sometimes denoted by ⊗, is an operation on two matrices of arbitrary size resulting in a block matrix.It is a specialization of the tensor product (which is denoted by the same symbol) from vectors to matrices and gives the matrix of the tensor product linear map with respect to a standard choice of basis.
Salome is a free software tool that provides a generic platform for pre- and post-processing for numerical simulation. Shogun , an open-source large-scale machine-learning toolbox that provides several SVM implementations (like libSVM, SVMlight) under a common framework and interfaces to Octave, MATLAB, Python, R
The gradient of a function is obtained by raising the index of the differential , whose components are given by: =; =; =, = = The divergence of a vector field with components is
In linear algebra, the outer product of two coordinate vectors is the matrix whose entries are all products of an element in the first vector with an element in the second vector.
The density matrix is a representation of a linear operator called the density operator.The density matrix is obtained from the density operator by a choice of an orthonormal basis in the underlying space. [2]
Input: initial guess x (0) to the solution, (diagonal dominant) matrix A, right-hand side vector b, convergence criterion Output: solution when convergence is reached Comments: pseudocode based on the element-based formula above k = 0 while convergence not reached do for i := 1 step until n do σ = 0 for j := 1 step until n do if j ≠ i then ...
The first vector space isomorphism on the list above, , gives the coordinate representation of an abstract tensor. Assume that each of the vector spaces has a basis {,, …,}.