Polar decompositionIn mathematics, the polar decomposition of a square real or complex matrix is a factorization of the form , where is a unitary matrix and is a positive semi-definite Hermitian matrix ( is an orthogonal matrix and is a positive semi-definite symmetric matrix in the real case), both square and of the same size. Intuitively, if a real matrix is interpreted as a linear transformation of -dimensional space , the polar decomposition separates it into a rotation or reflection of , and a scaling of the space along a set of orthogonal axes.
Chemical decompositionChemical decomposition, or chemical breakdown, is the process or effect of simplifying a single chemical entity (normal molecule, reaction intermediate, etc.) into two or more fragments. Chemical decomposition is usually regarded and defined as the exact opposite of chemical synthesis. In short, the chemical reaction in which two or more products are formed from a single reactant is called a decomposition reaction. The details of a decomposition process are not always well defined.
Chemical stabilityIn chemistry, chemical stability is the thermodynamic stability of a chemical system. Thermodynamic stability occurs when a system is in its lowest energy state, or in chemical equilibrium with its environment. This may be a dynamic equilibrium in which individual atoms or molecules change form, but their overall number in a particular form is conserved. This type of chemical thermodynamic equilibrium will persist indefinitely unless the system is changed. Chemical systems might undergo changes in the phase of matter or a set of chemical reactions.
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.
Chemical reactionA chemical reaction is a process that leads to the chemical transformation of one set of chemical substances to another. Classically, chemical reactions encompass changes that only involve the positions of electrons in the forming and breaking of chemical bonds between atoms, with no change to the nuclei (no change to the elements present), and can often be described by a chemical equation. Nuclear chemistry is a sub-discipline of chemistry that involves the chemical reactions of unstable and radioactive elements where both electronic and nuclear changes can occur.
Electrolysis of waterElectrolysis of water is using electricity to split water into oxygen (O2) and hydrogen (H2) gas by electrolysis. Hydrogen gas released in this way can be used as hydrogen fuel, but must be kept apart from the oxygen as the mixture would be extremely explosive. Separately pressurised into convenient 'tanks' or 'gas bottles', hydrogen can be used for oxyhydrogen welding and other applications, as the hydrogen / oxygen flame can reach circa 2,800°C. Water electrolysis requires a minimum potential difference of 1.
