This article lists
mathematical identities, that is, ''identically true relations'' holding in
mathematics.
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Bézout's identity
In mathematics, Bézout's identity (also called Bézout's lemma), named after Étienne Bézout, is the following theorem:
Here the greatest common divisor of and is taken to be . The integers and are called Bézout coefficients for ; they ...
(despite its usual name, it is not, properly speaking, an identity)
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Binomial inverse theorem
In mathematics (specifically linear algebra), the Woodbury matrix identity, named after Max A. Woodbury, says that the inverse of a rank-''k'' correction of some matrix can be computed by doing a rank-''k'' correction to the inverse of the origin ...
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Binomial identity
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Brahmagupta–Fibonacci two-square identity
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Candido's identity
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Cassini and Catalan identities
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Degen's eight-square identity In mathematics, Degen's eight-square identity establishes that the product of two numbers, each of which is a sum of eight squares, is itself the sum of eight squares.
Namely:
\begin
& \left(a_1^2+a_2^2+a_3^2+a_4^2+a_5^2+a_6^2+a_7^2+a_8^2\right)\le ...
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Difference of two squares
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Euler's four-square identity
In mathematics, Euler's four-square identity says that the product of two numbers, each of which is a sum of four squares, is itself a sum of four squares.
Algebraic identity
For any pair of quadruples from a commutative ring, the following expre ...
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Euler's identity
In mathematics, Euler's identity (also known as Euler's equation) is the equality
e^ + 1 = 0
where
: is Euler's number, the base of natural logarithms,
: is the imaginary unit, which by definition satisfies , and
: is pi, the ratio of the circ ...
* Fibonacci's identity see
Brahmagupta–Fibonacci identity
In algebra, the Brahmagupta–Fibonacci identity expresses the product of two sums of two squares as a sum of two squares in two different ways. Hence the set of all sums of two squares is closed under multiplication. Specifically, the identity say ...
or
Cassini and Catalan identities
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Heine's identity
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Hermite's identity
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Lagrange's identity
In algebra, Lagrange's identity, named after Joseph Louis Lagrange, is:
\begin
\left( \sum_^n a_k^2\right) \left(\sum_^n b_k^2\right) - \left(\sum_^n a_k b_k\right)^2 & = \sum_^ \sum_^n \left(a_i b_j - a_j b_i\right)^2 \\
& \left(= \frac \sum_^n ...
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Lagrange's trigonometric identities
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MacWilliams identity
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Matrix determinant lemma
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Newton's identity
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Parseval's identity In mathematical analysis, Parseval's identity, named after Marc-Antoine Parseval, is a fundamental result on the summability of the Fourier series of a function. Geometrically, it is a generalized Pythagorean theorem for inner-product spaces (which ...
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Pfister's sixteen-square identity In algebra, Pfister's sixteen-square identity is a non- bilinear identity of form
\left(x_1^2+x_2^2+x_3^2+\cdots+x_^2\right)\left(y_1^2+y_2^2+y_3^2+\cdots+y_^2\right) = z_1^2+z_2^2+z_3^2+\cdots+z_^2
It was first proven to exist by H. Zassenhaus a ...
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Sherman–Morrison formula
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Sophie Germain identity
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Sun's curious identity
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Sylvester's determinant identity
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Vandermonde's identity
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Woodbury matrix identity
Identities for classes of functions
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Exterior calculus identities
* Fibonacci identities:
Combinatorial Fibonacci identities and
Other Fibonacci identities
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Hypergeometric function identities
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List of integrals of logarithmic functions
The following is a list of integrals (antiderivative functions) of logarithmic functions. For a complete list of integral functions, see list of integrals.
''Note:'' ''x'' > 0 is assumed throughout this article, and the constant of integratio ...
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List of topics related to
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List of trigonometric identities
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Inverse trigonometric functions
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Logarithmic identities In mathematics, many logarithmic identities exist. The following is a compilation of the notable of these, many of which are used for computational purposes.
Trivial identities
:
Explanations
By definition, we know that:
:\color \log \color ...
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Summation identities
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Vector calculus identities
See also
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* {{annotated link, List of set identities and relations
External links
Encyclopedia of Equation Online encyclopedia of mathematical identities
A Collection of Algebraic Identities
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Identities