Coefficient
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In mathematics, a coefficient is a constant multiplicative factor of a certain object. For example, the coefficient of x 2 in 9x2 is 9.
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:
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:
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.
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
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
- Coefficient of Thermal Expansion (thermodynamics) (dimensionless) - Relates the change in temperature to the change in a material's dimensions.
- Partition Coefficient (KD) (chemistry) - The ratio of concentrations of a compound in two phases of a mixture of two immiscible solvents at equilibrium.
- 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.
- 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.
- 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.
- 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.
- 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.
See also
ca:Coeficient cs:Koeficient de:Koeffizient fr:Coefficient ko:계수 io:Koeficiento is:Stuðull (stærðfræði) nl:Coëfficiënt ja:係数 no:Koeffisientsimple:Coefficient sk:Matematický koeficient sl:Koeficient fi:Kerroin sv:Koefficient ur:عددی سر
Acknowledgement and Attribution Regarding Sources of Content
Some of the initial content on this page may be incorporated in part from copyleft sources in the public domain including wikis such as Wikipedia and AskDrWiki. Drug information for patients came from the The National Library of Medicine. Infectious disease information may have come from the Centers for Disease Control (CDC). Differential Diagnoses are drawn from clinicians as well as an amalgamation of 3 sources: 1.The Disease Database; 2. Kahan, Scott, Smith, Ellen G. In A Page: Signs and Symptoms. Malden, Massachusetts: Blackwell Publishing, 2004:3; 3. Sailer, Christian, Wasner, Susanne. Differential Diagnosis Pocket. Hermosa Beach, CA: Borm Bruckmeir Publishing LLC, 2002:7 .
