In physics, particularly in quantum perturbation theory, the matrix element refers to the linear operator of a modified Hamiltonian using Dirac notation...

Matrix element may refer to: The (scalar) entries of a matrix. Matrix element (physics), the value of a linear operator (especially a modified Hamiltonian)...

operation is matrix multiplication is called a matrix group. Since a group of every element must be invertible, the most general matrix groups are the...

set U = {u1, …, un}, the adjacency matrix is a square n × n matrix A such that its element Aij is one when there is an edge from vertex ui to vertex uj...

as well as in applied mathematics, statistics, physics, economics, and engineering. Computing matrix products is a central operation in all computational...

a Hermitian matrix (or self-adjoint matrix) is a complex square matrix that is equal to its own conjugate transpose—that is, the element in the i-th row...

rotation matrix is a transformation matrix that is used to perform a rotation in Euclidean space. For example, using the convention below, the matrix R = [...

is the n×n identity matrix. When X is an n×n diagonal matrix then exp(X) will be an n×n diagonal matrix with each diagonal element equal to the ordinary...

dynamic implicit and explicit finite element simulations of the native knee joint" (PDF). Medical Engineering & Physics. 38 (10): 1123–1130. doi:10.1016/j...

transpose of a matrix is an operator which flips a matrix over its diagonal; that is, it switches the row and column indices of the matrix A by producing...

probability theory and mathematical physics, a random matrix is a matrix-valued random variable—that is, a matrix in which some or all of its entries...

covariance matrix (also known as auto-covariance matrix, dispersion matrix, variance matrix, or variance–covariance matrix) is a square matrix giving the...

between states. In a transition-rate matrix Q {\displaystyle Q} (sometimes written A {\displaystyle A} ), element q i j {\displaystyle q_{ij}} (for i ≠...

purposes than tension. Stress is a 3x3 matrix called a tensor, and the σ 11 {\displaystyle \sigma _{11}} element of the stress tensor is tensile force...

In linear algebra, a diagonal matrix is a matrix in which the entries outside the main diagonal are all zero; the term usually refers to square matrices...

tensor index notation is preferred in physics. Two competing notational conventions split the field of matrix calculus into two separate groups. The...

Matrix mechanics is a formulation of quantum mechanics created by Werner Heisenberg, Max Born, and Pascual Jordan in 1925. It was the first conceptually...

paraxial rays. Each optical element (surface, interface, mirror, or beam travel) is described by a 2 × 2 ray transfer matrix which operates on a vector...

In physics, the S-matrix or scattering matrix relates the initial state and the final state of a physical system undergoing a scattering process. It is...

proportion of the first order term. Idempotent element (ring theory) Unipotent Reduced ring Nil ideal Nilpotent matrix Polcino Milies & Sehgal (2002), An Introduction...

It is also called a probability matrix, transition matrix, substitution matrix, or Markov matrix. The stochastic matrix was first developed by Andrey Markov...

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. If the two...

linear algebra, a skew-symmetric (or antisymmetric or antimetric) matrix is a square matrix whose transpose equals its negative. That is, it satisfies the...

Physics is a scientific discipline that seeks to construct and experimentally test theories of the physical universe. These theories vary in their scope...

neighborhoods of the identity element of the Lie group. In the case of the Lorentz group, the exponential map is just the matrix exponential. Globally, the...

theory, the Laplacian matrix, also called the graph Laplacian, admittance matrix, Kirchhoff matrix or discrete Laplacian, is a matrix representation of a...

high-dimensional matrix. Tensors have become important in physics because they provide a concise mathematical framework for formulating and solving physics problems...

Algebraic structure Scalar (physics) Linear algebra Matrix (mathematics) Row and column vectors Tensor Vector (mathematics and physics) Lay, David C. (2006)...

In linear algebra, an orthogonal matrix, or orthonormal matrix, is a real square matrix whose columns and rows are orthonormal vectors. One way to express...

In linear algebra, a minor of a matrix A is the determinant of some smaller square matrix, cut down from A by removing one or more of its rows and columns...