Orthonormal basisIn mathematics, particularly linear algebra, an orthonormal basis for an inner product space V with finite dimension is a basis for whose vectors are orthonormal, that is, they are all unit vectors and orthogonal to each other. For example, the standard basis for a Euclidean space is an orthonormal basis, where the relevant inner product is the dot product of vectors. The of the standard basis under a rotation or reflection (or any orthogonal transformation) is also orthonormal, and every orthonormal basis for arises in this fashion.
Invertible matrixIn linear algebra, an n-by-n square matrix A is called invertible (also nonsingular, nondegenerate or (rarely used) regular), if there exists an n-by-n square matrix B such that where In denotes the n-by-n identity matrix and the multiplication used is ordinary matrix multiplication. If this is the case, then the matrix B is uniquely determined by A, and is called the (multiplicative) inverse of A, denoted by A−1. Matrix inversion is the process of finding the matrix B that satisfies the prior equation for a given invertible matrix A.
Nuclear fusionNuclear fusion is a reaction in which two or more atomic nuclei, usually deuterium and tritium (hydrogen variants), are combined to form one atomic nuclei and subatomic particles (neutrons or protons). The difference in mass between the reactants and products is manifested as either the release or absorption of energy. This difference in mass arises due to the difference in nuclear binding energy between the atomic nuclei before and after the reaction.
Singular value decompositionIn linear algebra, the singular value decomposition (SVD) is a factorization of a real or complex matrix. It generalizes the eigendecomposition of a square normal matrix with an orthonormal eigenbasis to any matrix. It is related to the polar decomposition. Specifically, the singular value decomposition of an complex matrix M is a factorization of the form where U is an complex unitary matrix, is an rectangular diagonal matrix with non-negative real numbers on the diagonal, V is an complex unitary matrix, and is the conjugate transpose of V.
Underdetermined systemIn mathematics, a system of linear equations or a system of polynomial equations is considered underdetermined if there are fewer equations than unknowns (in contrast to an overdetermined system, where there are more equations than unknowns). The terminology can be explained using the concept of constraint counting. Each unknown can be seen as an available degree of freedom. Each equation introduced into the system can be viewed as a constraint that restricts one degree of freedom.
Dense plasma focusA dense plasma focus (DPF) is a type of plasma generating system originally developed as a fusion power device starting in the early 1960s. The system demonstrated scaling laws that suggested it would not be useful in the commercial power role, and since the 1980s it has been used primarily as a fusion teaching system, and as a source of neutrons and X-rays. The original concept was developed in 1954 by N.V. Filippov, who noticed the effect while working on early pinch machines in the USSR.
Density functional theoryDensity-functional theory (DFT) is a computational quantum mechanical modelling method used in physics, chemistry and materials science to investigate the electronic structure (or nuclear structure) (principally the ground state) of many-body systems, in particular atoms, molecules, and the condensed phases. Using this theory, the properties of a many-electron system can be determined by using functionals, i.e. functions of another function. In the case of DFT, these are functionals of the spatially dependent electron density.
Inertial confinement fusionInertial confinement fusion (ICF) is a fusion energy process that initiates nuclear fusion reactions by compressing and heating targets filled with fuel. The targets are small pellets, typically containing deuterium (2H) and tritium (3H). Energy is deposited in the target's outer layer, which explodes outward. This produces a reaction force in the form of shock waves that travel through the target. The waves compress and heat it. Sufficiently powerful shock waves generate fusion.
Fusion energy gain factorA fusion energy gain factor, usually expressed with the symbol Q, is the ratio of fusion power produced in a nuclear fusion reactor to the power required to maintain the plasma in steady state. The condition of Q = 1, when the power being released by the fusion reactions is equal to the required heating power, is referred to as breakeven, or in some sources, scientific breakeven. The energy given off by the fusion reactions may be captured within the fuel, leading to self-heating.
Basis (linear algebra)In mathematics, a set B of vectors in a vector space V is called a basis (: bases) if every element of V may be written in a unique way as a finite linear combination of elements of B. The coefficients of this linear combination are referred to as components or coordinates of the vector with respect to B. The elements of a basis are called . Equivalently, a set B is a basis if its elements are linearly independent and every element of V is a linear combination of elements of B.
