LU decompositionIn numerical analysis and linear algebra, lower–upper (LU) decomposition or factorization factors a matrix as the product of a lower triangular matrix and an upper triangular matrix (see matrix decomposition). The product sometimes includes a permutation matrix as well. LU decomposition can be viewed as the matrix form of Gaussian elimination. Computers usually solve square systems of linear equations using LU decomposition, and it is also a key step when inverting a matrix or computing the determinant of a matrix.
QR decompositionIn linear algebra, a QR decomposition, also known as a QR factorization or QU factorization, is a decomposition of a matrix A into a product A = QR of an orthonormal matrix Q and an upper triangular matrix R. QR decomposition is often used to solve the linear least squares problem and is the basis for a particular eigenvalue algorithm, the QR algorithm. Any real square matrix A may be decomposed as where Q is an orthogonal matrix (its columns are orthogonal unit vectors meaning ) and R is an upper triangular matrix (also called right triangular matrix).
Cholesky decompositionIn linear algebra, the Cholesky decomposition or Cholesky factorization (pronounced ʃəˈlɛski ) is a decomposition of a Hermitian, positive-definite matrix into the product of a lower triangular matrix and its conjugate transpose, which is useful for efficient numerical solutions, e.g., Monte Carlo simulations. It was discovered by André-Louis Cholesky for real matrices, and posthumously published in 1924. When it is applicable, the Cholesky decomposition is roughly twice as efficient as the LU decomposition for solving systems of linear equations.
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.
Energy transitionAn energy transition (or energy system transformation) is a significant structural change in an energy system regarding supply and consumption. Currently, a transition to sustainable energy (mostly renewable energy) is underway to limit climate change. It is also called renewable energy transition. The current transition is driven by a recognition that global greenhouse-gas emissions must be drastically reduced. This process involves phasing-down fossil fuels and re-developing whole systems to operate on low carbon electricity.
Fossil fuel subsidiesFossil fuel subsidies are energy subsidies on fossil fuels. They may be tax breaks on consumption, such as a lower sales tax on natural gas for residential heating; or subsidies on production, such as tax breaks on exploration for oil. Or they may be free or cheap negative externalities; such as air pollution or climate change due to burning gasoline, diesel and jet fuel. Some fossil fuel subsidies are via electricity generation, such as subsidies for coal-fired power stations.
Fossil fuel phase-outFossil fuel phase-out is the gradual reduction of the use and production of fossil fuels to zero, to reduce deaths and illness from air pollution, limit climate change, and strengthen energy independence. It is part of the ongoing renewable energy transition. Although many countries are shutting down coal-fired power stations, electricity generation is not moving off coal fast enough to meet climate goals. Many countries have set dates to stop selling petrol and diesel cars and trucks, but a timetable to stop burning fossil gas has not yet been agreed.
Fossil fuels lobbyThe fossil fuels lobby includes paid representatives of corporations involved in the fossil fuel industry (oil, gas, coal), as well as related industries like chemicals, plastics, aviation and other transportation. Because of their wealth and the importance of energy, transport and chemical industries to local, national and international economies, these lobbies have the capacity and money to attempt to have outsized influence governmental policy.
Carbon taxA carbon tax is a tax levied on the carbon emissions required to produce goods and services. Carbon taxes are intended to make visible the "hidden" social costs of carbon emissions, which are otherwise felt only in indirect ways like more severe weather events. In this way, they are designed to reduce greenhouse gas emissions by increasing prices of the fossil fuels that emit them when burned. This both decreases demand for goods and services that produce high emissions and incentivizes making them less carbon-intensive.
Fossil fuelA fossil fuel is a hydrocarbon-containing material such as coal, oil, and natural gas, formed naturally in the Earth's crust from the remains of dead plants and animals that is extracted and burned as a fuel. Fossil fuels may be burned to provide heat for use directly (such as for cooking or heating), to power engines (such as internal combustion engines in motor vehicles), or to generate electricity. Some fossil fuels are refined into derivatives such as kerosene, gasoline and propane before burning.
