Transformation matrixIn linear algebra, linear transformations can be represented by matrices. If is a linear transformation mapping to and is a column vector with entries, then for some matrix , called the transformation matrix of . Note that has rows and columns, whereas the transformation is from to . There are alternative expressions of transformation matrices involving row vectors that are preferred by some authors. Matrices allow arbitrary linear transformations to be displayed in a consistent format, suitable for computation.
Hermitian matrixIn mathematics, 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 and j-th column is equal to the complex conjugate of the element in the j-th row and i-th column, for all indices i and j: or in matrix form: Hermitian matrices can be understood as the complex extension of real symmetric matrices.
Covariance matrixIn probability theory and statistics, a covariance matrix (also known as auto-covariance matrix, dispersion matrix, variance matrix, or variance–covariance matrix) is a square matrix giving the covariance between each pair of elements of a given random vector. Any covariance matrix is symmetric and positive semi-definite and its main diagonal contains variances (i.e., the covariance of each element with itself). Intuitively, the covariance matrix generalizes the notion of variance to multiple dimensions.
Julian (emperor)Julian (Flavius Claudius Julianus; Ἰουλιανός Ioulianos; 331 – 26 June 363) was Roman emperor from 361 to 363, as well as a notable philosopher and author in Greek. His rejection of Christianity, and his promotion of Neoplatonic Hellenism in its place, caused him to be remembered as Julian the Apostate in Christian tradition. A nephew of Constantine the Great, Julian was one of few in the imperial family to survive the purges and civil wars during the reign of Constantius II, his cousin.
École Polytechnique Fédérale de LausanneThe École polytechnique fédérale de Lausanne (EPFL; English: Swiss Federal Institute of Technology in Lausanne; Eidgenössische Technische Hochschule Lausanne) is a public research university in Lausanne, Switzerland. Established in 1853, EPFL has placed itself as a university specializing in engineering and natural sciences. EPFL is part of the ETH Domain, which is directly dependent on the Federal Department of Economic Affairs, Education and Research.
Diagonalizable matrixIn linear algebra, a square matrix is called diagonalizable or non-defective if it is similar to a diagonal matrix, i.e., if there exists an invertible matrix and a diagonal matrix such that , or equivalently . (Such , are not unique.) For a finite-dimensional vector space , a linear map is called diagonalizable if there exists an ordered basis of consisting of eigenvectors of .
Roman–Persian WarsThe Roman–Persian Wars, also known as the Roman–Iranian Wars, were a series of conflicts between states of the Greco-Roman world and two successive Iranian empires: the Parthian and the Sasanian. Battles between the Parthian Empire and the Roman Republic began in 54 BC; wars began under the late Republic, and continued through the Roman (later Eastern Roman (Byzantine)) and Sasanian empires. A plethora of vassal kingdoms and allied nomadic nations in the form of buffer states and proxies also played a role.
CoefficientIn mathematics, a coefficient is a multiplicative factor involved in some term of a polynomial, a series, or an expression. It may be a number (dimensionless), in which case it is known as a numerical factor. It may also be a constant with units of measurement, in which it is known as a constant multiplier. In general, coefficients may be any expression (including variables such as a, b and c). When the combination of variables and constants is not necessarily involved in a product, it may be called a parameter.
Input/outputIn computing, input/output (I/O, i/o, or informally io or IO) is the communication between an information processing system, such as a computer, and the outside world, possibly a human or another information processing system. Inputs are the signals or data received by the system and outputs are the signals or data sent from it. The term can also be used as part of an action; to "perform I/O" is to perform an input or output operation. are the pieces of hardware used by a human (or other system) to communicate with a computer.
Heat transfer coefficientIn thermodynamics, the heat transfer coefficient or film coefficient, or film effectiveness, is the proportionality constant between the heat flux and the thermodynamic driving force for the flow of heat (i.e., the temperature difference, ΔT ). It is used in calculating the heat transfer, typically by convection or phase transition between a fluid and a solid. The heat transfer coefficient has SI units in watts per square meter per kelvin (W/m2/K).
Mass transfer coefficientIn engineering, the mass transfer coefficient is a diffusion rate constant that relates the mass transfer rate, mass transfer area, and concentration change as driving force: Where: is the mass transfer coefficient [mol/(s·m2)/(mol/m3)], or m/s is the mass transfer rate [mol/s] is the effective mass transfer area [m2] is the driving force concentration difference [mol/m3]. This can be used to quantify the mass transfer between phases, immiscible and partially miscible fluid mixtures (or between a fluid and a porous solid).
