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Encyclopedia > Coefficient

In mathematics, a coefficient is a constant multiplicative factor of a certain object. For example, the coefficient in 9x2 is 9. Look up coefficient in Wiktionary, the free dictionary. ... For other meanings of mathematics or uses of math and maths, see Mathematics (disambiguation) and Math (disambiguation). ... In mathematics and the mathematical sciences, a constant is a fixed, but possibly unspecified, value. ... In mathematics, multiplication is an elementary arithmetic operation. ...


The object can be such things as a variable, a vector, a function, etc. In some cases, the objects and the coefficients are indexed in the same way, leading to expressions such as: In computer science and mathematics, a variable (IPA pronunciation: ) (sometimes called a pronumeral) is a symbolic representation denoting a quantity or expression. ... A vector going from A to B. In physics and in vector calculus, a spatial vector, or simply vector, is a concept characterized by a magnitude and a direction. ... Graph of example function, The mathematical concept of a function expresses the intuitive idea of deterministic dependence between two quantities, one of which is viewed as primary (the independent variable, argument of the function, or its input) and the other as secondary (the value of the function, or output). A...

a_1 x_1 + a_2 x_2 + a_3 x_3 + cdots

where an is the coefficient of the variable xn for each n = 1, 2, 3, …


In a polynomial P(x) of one variable x, the coefficient of xk can be indexed by k, giving the convention that for example: In mathematics, a polynomial is an expression that is constructed from one variable or more variables and constants, using only the operations of addition, subtraction, multiplication, and constant positive whole number exponents. ...

P(x) = a_k x^k + cdots + a_1 x^1 + a_0.

For the largest k where ak ≠ 0, ak is called the leading coefficient of P because most often, polynomials are written from the largest power of x, downward (i.e. x5 + x4 + x2 ...).


Important coefficients in mathematics include the binomial coefficients which are coefficients in the statement of the binomial theorem. These can be partially found with Pascal's triangle. In mathematics, particularly in combinatorics, a binomial coefficient is a coefficient of any of the terms in the expansion of the binomial (x+1)n. ... In mathematics, the binomial theorem is an important formula giving the expansion of powers of sums. ... The first five rows of Pascals triangle In mathematics, Pascals triangle is a geometric arrangement of the binomial coefficients in a triangle. ...


Linear algebra

In linear algebra, the leading coefficient of a row in a matrix is the first nonzero entry in that row. So, for example, given Linear algebra is the branch of mathematics concerned with the study of vectors, vector spaces (also called linear spaces), linear maps (also called linear transformations), and systems of linear equations. ...

M = begin{bmatrix}1 & 2 & 0 & 6  0 & 2 & 9 & 4  0 & 0 & 0 & 4  0 & 0 & 0 & 0 end{bmatrix}

1 is the leading coefficient of the first row, 2 is the leading coefficient of the second row, 4 is the leading coefficient of the third row, and the last row does not have a leading coefficient.


Examples of Physical Coefficients

  1. Coefficient of Thermal Expansion (thermodynamics) (dimensionless) - Relates the change in temperature to the change in a material's dimensions.
  1. Partition Coefficient (KD) (chemistry)- The ratio of concentrations of a compound in two phases of a mixture of two immiscible solvents at equilibrium.
  1. Hall coefficient (electrical physics) - Relates a magnetic field applied to an element to the voltage created, the amount of current and the element thickness. It is a characteristic of the material from which the conductor is made.
  1. Lift Coefficient (CL or CZ) (Aerodynamics) (dimensionless)- Relates the lift generated by an airfoil with the dynamic pressure of the fluid flow around the airfoil, and the planform area of the airfoil.
  1. Ballistic coefficient (BC) (Aerodynamics) (units of kg/m²) - A measure of a body's ability to overcome air resistance in flight. BC is a function of mass, diameter, and drag coefficient.
  1. Transmission Coefficient (quantum mechanics) (dimensionless) - Represents the probability flux of a transmitted wave relative to that of an incident wave. It is often used to describe the probability of a particle tunnelling through a barrier.
  1. Damping Factor A.K.A. viscous damping coefficient (Physical Engineering) (units of Newton-seconds per meter) - relates a damping force with the velocity of the object whose motion is being dampened.

During heat transfer, the energy that is stored in the intermolecular bonds between atoms changes. ... Thermodynamics (from the Greek θερμη, therme, meaning heat and δυναμις, dynamis, meaning power) is a branch of physics that studies the effects of changes in temperature, pressure, and volume on physical systems at the macroscopic scale by analyzing the collective motion of their particles using statistics. ... A partition coefficient is a measure of differential solubility of a compound in two solvents. ... For other uses, see Chemistry (disambiguation). ... Hall effect diagram, showing electron flow (rather than conventional current). ... The lift coefficient (CL) is a number associated with a particular shape of an airfoil, and is incorporated in the lift equation to predict the lift force generated by a wing using this particular cross section. ... For the Daft Punk song, see Aerodynamic (song). ... The ballistic coefficient (BC) is the mass of the object divided by the diameter squared that it presents to the airflow divided by a dimensionless constant i that relates to the shape. ... The transmission coefficient, , for a particle tunneling through a single barrier potential is found to be: Where are the 2 classical turning points for the potential barrier. ... For a less technical and generally accessible introduction to the topic, see Introduction to quantum mechanics. ... In quantum mechanics, quantum tunnelling is a micro and nanoscopic phenomenon in which a particle violates principles of classical mechanics by penetrating or passing through a potential barrier or impedance higher than the kinetic energy of the particle. ... Damping is any effect, either deliberately engendered or inherent to a system, that tends to reduce the amplitude of oscillations of an oscillatory system. ...

See also


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