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In mathematics, a matrix coefficient (or matrix element) is a function on a group of a special form, which depends on a linear representation of the group and additional data. Precisely, it is a function on a compact topological group G obtained by composing a representation of G on a vector space V with a linear map from the endomorphisms of V ...
The second method is used when the number of elements in each row is the same and known at the time the program is written. The programmer declares the array to have, say, three columns by writing e.g. elementtype tablename[][3];. One then refers to a particular element of the array by writing tablename[first index][second index]. The compiler ...
Note how the use of A[i][j] with multi-step indexing as in C, as opposed to a neutral notation like A(i,j) as in Fortran, almost inevitably implies row-major order for syntactic reasons, so to speak, because it can be rewritten as (A[i])[j], and the A[i] row part can even be assigned to an intermediate variable that is then indexed in a separate expression.
In computer programming, array slicing is an operation that extracts a subset of elements from an array and packages them as another array, possibly in a different dimension from the original.
Matrix mechanics is a formulation of quantum mechanics created by Werner Heisenberg, Max Born, and Pascual Jordan in 1925. It was the first conceptually autonomous and logically consistent formulation of quantum mechanics.
This makes calculating the matrix elements of the interaction Hamiltonian very important for finding the energy levels and wave-functions of particles in a different atomic elements and nuclide. This many-body Hamiltonian problem becomes very complicated with the addition of more electrons, protons and neutrons as we go to other elements in the ...
The geometric-distance matrix of a molecular structure G is a real symmetric n x n matrix defined in the same way as a 2-D matrix. However, the matrix elements D ij will hold a collection of shortest Cartesian distances between i and j in G. Also known as topographic matrix, the geometric-distance matrix can be constructed from the known ...
An circulant matrix takes the form = [] or the transpose of this form (by choice of notation). If each c i {\displaystyle c_{i}} is a p × p {\displaystyle p\times p} square matrix , then the n p × n p {\displaystyle np\times np} matrix C {\displaystyle C} is called a block-circulant matrix .