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Symbolab is an answer engine [1] that provides step-by-step solutions to mathematical problems in a range of subjects. [2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011. In 2020, the company was acquired by American educational technology website Course Hero. [3] [4]
A multilinear map of one variable is a linear map, and of two variables is a bilinear map. More generally, for any nonnegative integer , a multilinear map of k variables is called a k-linear map. If the codomain of a multilinear map is the field of scalars, it is called a multilinear form.
A map is a function, as in the association of any of the four colored shapes in X to its color in Y. In mathematics, a map or mapping is a function in its general sense. [1] These terms may have originated as from the process of making a geographical map: mapping the Earth surface to a sheet of paper. [2]
In mathematics, and more specifically in linear algebra, a linear map (also called a linear mapping, linear transformation, vector space homomorphism, or in some contexts linear function) is a mapping between two vector spaces that preserves the operations of vector addition and scalar multiplication.
Functions that maximize or minimize functionals may be found using the Euler–Lagrange equation of the calculus of variations. A simple example of such a problem is to find the curve of shortest length connecting two points. If there are no constraints, the solution is a straight line between the points. However, if the curve is constrained to ...
Here the exp-notation is used for the exponential mapping of the Lie algebra and the calculus-style notation in the fraction indicates the usual formal series expansion. For more information and two full proofs in the general case, see the freely available Sternberg (2004) reference.
The ZW-calculus was developed alongside the ZX-calculus, and can naturally describe the W-state and Fermionic quantum computing. [ 26 ] [ 27 ] It was the first graphical language which had a complete rule-set for an approximately universal set of linear maps between qubits, [ 8 ] and the early completeness results of the ZX-calculus use a ...
Stencils are classified into two categories: compact and non-compact, the difference being the layers from the point of interest that are also used for calculation. In the notation used for one-dimensional stencils n-1, n, n+1 indicate the time steps where timestep n and n-1 have known solutions and time step n+1 is to be calculated.