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Information about Coefficient

For other senses of this word, see coefficient (disambiguation).


In mathematics, a coefficient is a constant multiplicative factor of a certain object. For example, the coefficient 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.

Physics

In physics, many equations have coefficients associated with them. For example, is the coefficient of friction between two objects in the equation .

See also

Coefficient could have one of the following meanings:
  • In mathematics, a coefficient is a constant multiplicati of a function was once called its differential coefficient, a usage now mostly displaced by the modern term.

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Mathematics (colloquially, maths or math) is the body of knowledge centered on such concepts as quantity, structure, space, and change, and also the academic discipline that studies them. Benjamin Peirce called it "the science that draws necessary conclusions".
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In mathematics and the mathematical sciences, a constant is a fixed, but possibly unspecified, value. This is in contrast to a variable, which is not fixed.

Unspecified constants

The most widely mentioned sort of constant
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Multiplication is the mathematical operation of adding together multiple copies of the same number. For example, four multiplied by three is twelve, since three sets of four make twelve:


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variable (IPA pronunciation: [ˈvæɹiəbl]) (sometimes called a pronumeral) is a symbolic representation denoting a quantity or expression.
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spatial vector, or simply vector, is a concept characterized by a magnitude and a direction. A vector can be thought of as an arrow in Euclidean space, drawn from an initial point A pointing to a terminal point B.
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function expresses dependence between two quantities, one of which is given (the independent variable, argument of the function, or its "input") and the other produced (the dependent variable, value of the function, or "output").
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In mathematics, a polynomial is an expression that is constructed from one or more variables and constants, using only the operations of addition, subtraction, multiplication, and constant positive whole number exponents. is a polynomial.
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In mathematics, particularly in combinatorics, a binomial coefficient is a coefficient of any of the terms in the expansion of the binomial (x+y)n.
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In mathematics, the binomial theorem is an important formula giving the expansion of powers of sums. Its simplest version says



whenever n is any non-negative integer, the number


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Pascal's triangle is a geometric arrangement of the binomial coefficients in a triangle. It is named after Blaise Pascal in much of the western world, although other mathematicians studied it centuries before him in India, Persia, China, and Italy.
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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.
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Physics is the science of matter[1] and its motion[2][3], as well as space and time[4][5] —the science that deals with concepts such as force, energy, mass, and charge.
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The coefficient of friction is a dimensionless quantity used to calculate the force of friction (static or kinetic).

The coefficient of static friction is defined as the ratio of the maximum static friction force (F
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The degree of a polynomial is the maximum of the degrees of all terms in the polynomial. For example, in 2x3 + 4x2 + x + 7, the term of highest degree is 2x3; therefore the polynomial is said to have
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In mathematics, a polynomial is an expression that is constructed from one or more variables and constants, using only the operations of addition, subtraction, multiplication, and constant positive whole number exponents. is a polynomial.
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