# coefficient

A coefficient ((new) lat. Coefficiens / coëfficiens , a noun of the PPA from the lat. Coefficere "participate", formed by Franciscus Vieta ), also known as an initial number or pre- number, is a number or variable added to another arithmetic expression as a factor . The coefficient can be a parameter or a key figure (physics, economics). In analysis it appears in monomials .

## mathematics

In mathematics , a coefficient is a factor that belongs to a specific object such as a variable or a basis vector . Typically, objects and coefficients are indexed in the same order, so expressions like

${\ displaystyle a_ {1} x_ {1} + a_ {2} x_ {2} + a_ {3} x_ {3} + \ dotsb}$

result, with as the coefficient of the variable for each${\ displaystyle a_ {n}}$${\ displaystyle x_ {n}}$${\ displaystyle n = 1,2,3, \ dotsc}$

Simple example: The coefficient of the term is . ${\ displaystyle 9x ^ {2}}$${\ displaystyle 9}$

Examples of important mathematical coefficients:

## physics

In physics , a coefficient is often, but not always, a quantity in the dimension number that describes a property of certain materials, bodies or systems. In older technical literature, coefficients are also called coefficients . Examples:

Far from every physical constant of the dimension number is called a coefficient. Counterexamples:

Examples of dimensional coefficients:

## chemistry

### Stoichiometry

In stoichiometry , the stoichiometric coefficient indicates in a reaction equation how many particles or moles of a substance react with how many particles or moles of other substances. If the coefficient is 1, it is omitted.

Example ( oxyhydrogen reaction ):
${\ displaystyle \ mathrm {2 \ H_ {2} + O_ {2} \ longrightarrow 2 \ H_ {2} O}}$
Hydrogen and water have the stoichiometric coefficient 2 because
• 2 hydrogen molecules react with one oxygen molecule to form 2 water molecules
• 2 moles of hydrogen react with one mole of oxygen to form 2 moles of water.

### Physical chemistry and biochemistry

• Binding coefficient (synonym coefficient of preferential interaction , English preferential interaction coefficient)

## Sports

In sporting associations such. B. UEFA also has coefficients which clubs or teams rate based on their previous successes.