In the algebra, Lagrange's identity, named after Joseph Louis Lagrange, is: ( ∑ k = 1 n a k 2 ) ( ∑ k = 1 n b k 2 ) − ( ∑ k = 1 n a k b k ) 2 = ∑ i = 1...

Lagrange's identity may refer to: Lagrange's identity, an algebraic identity Lagrange's identity (boundary value problem), an identity in calculus Lagrange's...

formula, also sometimes called Lagrange's identity, which is the three dimensional case of the Binet–Cauchy identity: ( a × b ) ⋅ ( c × d ) ≡ ( a ⋅ c...

associated boundary value problems in mathematics, Lagrange's identity, named after Joseph Louis Lagrange, gives the boundary terms arising from integration...

of Euler's four-square identity, and also of Lagrange's identity. Brahmagupta proved and used a more general Brahmagupta identity, stating ( a 2 + n b 2...

Brahmagupta–Fibonacci identity or Cassini and Catalan identities Heine's identity Hermite's identity Lagrange's identity Lagrange's trigonometric identities List of...

\left|H\right|.} Lagrange's theorem can be extended to the equation of indexes between three subgroups of G. Extension of Lagrange's theorem—If H is a...

U\\\end{matrix}}\right.} Green's function Kirchhoff integral theorem Lagrange's identity (boundary value problem) Strauss, Walter. Partial Differential Equations:...

theory) Lagrange's theorem (number theory) Lagrange's four-square theorem Lagrange's trigonometric identities Lagrange point colonization Lagrange (crater)...

elements of a commutative ring). Setting ai = ci and bj = dj, it gives Lagrange's identity, which is a stronger version of the Cauchy–Schwarz inequality for...

four-square identity, related to quaternions in the same way Lagrange's identity Other Parseval's identity Pythagorean trigonometric identity acceleration...

faithful quantification of multiparticle pure state entanglement using Lagrange's identity and wedge product". Quantum Information Processing. 16 (5): 118....

from Lagrange's identity[moved resource?] as applied in classical gravitational dynamics, the original form of which was included in Lagrange's "Essay...

Various Formulas in Electrostatics and Electromagnetism Using Lagrange's Trigonometric Identities". American Journal of Physics. 21 (2): 140. Bibcode:1953AmJPh...

of the starting point. Lagrange solved this problem in 1755 and sent the solution to Euler. Both further developed Lagrange's method and applied it to...

expressed in terms of the first fundamental form with the assistance of Lagrange's identity, d A = | X u × X v |   d u d v = ⟨ X u , X u ⟩ ⟨ X v , X v ⟩ − ⟨...

physics. A related identity regarding gradients and useful in vector calculus is Lagrange's formula of vector cross-product identity: ∇ × ( ∇ × A ) = ∇...

)+\mathbf {B} \times (\mathbf {C} \times \mathbf {A} )=\mathbf {0} .} Lagrange's identity: | A × B | 2 = ( A ⋅ A ) ( B ⋅ B ) − ( A ⋅ B ) 2 {\displaystyle |\mathbf...

Lagrange's four-square theorem, also known as Bachet's conjecture, states that every nonnegative integer can be represented as a sum of four non-negative...

Geometric algebra is an extension of vector algebra, providing additional algebraic structures on vector spaces, with geometric interpretations. Vector...

. {\displaystyle A(D)=\iint _{D}{\sqrt {EG-F^{2}}}\,du\,dv.} By Lagrange's identity, the expression under the square root is precisely | r u × r v |...

Beltrami identity, named after Eugenio Beltrami, is a special case of the Euler–Lagrange equation in the calculus of variations. The Euler–Lagrange equation...

is named after Joseph Louis Lagrange, although it was in fact invented by Euler and popularized by the former. In Lagrange's notation, a prime mark denotes...

faithful quantification of multiparticle pure state entanglement using Lagrange's identity and wedge product". Quantum Information Processing. 16 (5): 118....

basis, the Lagrange basis, L ( x ) = ∑ j = 0 k l j ( x ) y j {\textstyle L(x)=\sum _{j=0}^{k}l_{j}(x)y_{j}} , we merely get the identity matrix, δ i...

which holds if and only if the span of v and w is degenerate. By Lagrange's identity, this holds if and only if (v · w)2 = (v · v)(w · w) = 1, i.e., if...

finite loop Q is said to have the Lagrange property if the order of every subloop of Q divides the order of Q. Lagrange's theorem in group theory states...

absolute value denotes the length of a vector in Euclidean space. By Lagrange's identity for the cross product, the integral can be written ∬ D ( r → u ⋅...

streamfunction) are defined: The two-dimensional (or Lagrange) stream function, introduced by Joseph Louis Lagrange in 1781, is defined for incompressible (divergence-free)...

the above). It can be verified with elementary algebra. The identity was used by Lagrange to prove his four square theorem. More specifically, it implies...