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searching for Linear independence 34 found (83 total)

System of differential equations (1,160 words) [view diff] no match in snippet view article find links to article

In mathematics, a system of differential equations is a finite set of differential equations. Such a system can be either linear or non-linear. Also, such

Basis (universal algebra) (2,000 words) [view diff] exact match in snippet view article

outer condition exactly are the ones that provide the spanning and linear independence properties with linear combinations ℓ ( b ) = c 0 b 0 + c 1 b 1 +

Yunqing Tang (677 words) [view diff] exact match in snippet view article find links to article

Also in collaboration with Dimitrov and Calegari, she proved the linear independence of 1 , ζ ( 2 ) , {\displaystyle 1,\zeta (2),} and L ( 2 , χ − 3 )

Baker's theorem (3,411 words) [view diff] exact match in snippet view article find links to article

{2}}} . Although proving this result of "rational linear independence implies algebraic linear independence" for two elements of L {\displaystyle \mathbb

Frank Calegari (718 words) [view diff] exact match in snippet view article find links to article

denominators. Also in collaboration with Dimitrov and Tang, he proved the linear independence of 1, ζ(2), and L(2,χ−3). Calegari held a 5-year American Institute

E-function (611 words) [view diff] exact match in snippet view article find links to article

the algebraic independence of classes of numbers rather than just linear independence. Since then these functions have proved somewhat useful in number

Transcendental extension (1,682 words) [view diff] exact match in snippet view article find links to article

other hand. This analogy can be made more formal, by observing that linear independence in vector spaces and algebraic independence in field extensions both

Integral domain (3,124 words) [view diff] exact match in snippet view article find links to article

i ¯ g i = 0 {\textstyle \sum {\overline {h_{i}}}g_{i}=0} and, by linear independence, f i ¯ = 0 {\displaystyle {\overline {f_{i}}}=0} for all i {\displaystyle

Jacobson density theorem (1,139 words) [view diff] exact match in snippet view article find links to article

implies that x would be in the D-span of Y, contradicting the D-linear independence of X, therefore x • I ≠ 0. Since U is simple, we have: x • I = U

Singleton bound (1,544 words) [view diff] exact match in snippet view article find links to article

{n}{w}}(q-1)\sum _{j=0}^{w-d}(-1)^{j}{\binom {w-1}{j}}q^{w-d-j}.} The linear independence of the columns of a generator matrix of an MDS code permits a construction

Squaring the circle (4,922 words) [view diff] exact match in snippet view article find links to article

extend this argument, through the Lindemann–Weierstrass theorem on linear independence of algebraic powers of e {\displaystyle e} , to show that π {\displaystyle

Beresford Parlett (832 words) [view diff] case mismatch in snippet view article find links to article

University of California, Berkeley Thesis I. Bundles of Matrices and the Linear Independence of Their Minors; II. Applications of Laguerre's Method to the Matrix

Greedoid (1,730 words) [view diff] exact match in snippet view article find links to article

Zbl 0784.05002. Whitney, Hassler (1935), "On the abstract properties of linear independence", American Journal of Mathematics, 57 (3): 509–533, doi:10.2307/2371182

Mean transverse energy (585 words) [view diff] exact match in snippet view article find links to article

involving the cathode, the laser, and the extraction field. Due to the linear independence of the laser spot size and the MTE, the beam size is often factored

Sectional curvature (3,104 words) [view diff] exact match in snippet view article find links to article

u ⟩ . {\displaystyle \langle R(u,v)v,u\rangle .} Note that the linear independence of u and v forces the denominator in the above expression to be nonzero

Covariant derivative (6,478 words) [view diff] exact match in snippet view article find links to article

regular,[clarification needed] the compatibility condition implies linear independence of the partial derivative tangent vectors.) For a tangent vector

Super envy-freeness (502 words) [view diff] exact match in snippet view article find links to article

intervals). The matrix should be invertible - this is a witness to the linear independence of the measures. Using such a matrix, the algorithm partitions each

Chinese remainder theorem (7,239 words) [view diff] exact match in snippet view article find links to article

as an inverse limit of all such maps. Dedekind's theorem on the linear independence of characters. Let M be a monoid and k an integral domain, viewed

Variation of parameters (3,989 words) [view diff] exact match in snippet view article find links to article

root, we have to introduce a factor of x for one solution to ensure linear independence: u 1 = e − 2 x {\displaystyle u_{1}=e^{-2x}} and u 2 = x e − 2 x

Liouville–Arnold theorem (1,131 words) [view diff] exact match in snippet view article find links to article

) {\displaystyle F=(F_{1},\cdots ,F_{n})} , satisfying (Generic) linear independence: d F 1 ∧ ⋯ ∧ d F n ≠ 0 {\displaystyle dF_{1}\wedge \cdots \wedge

Natural logarithm of 2 (3,125 words) [view diff] exact match in snippet view article find links to article

Math. E-Notes. 7: 237–246. MR 2346048. Wu, Qiang (2003). "On the linear independence measure of logarithms of rational numbers". Mathematics of Computation

Lindemann–Weierstrass theorem (4,778 words) [view diff] exact match in snippet view article find links to article

where the αi exponents are required to be rational integers and linear independence is only assured over the rational integers, a result sometimes referred

Affine connection (7,683 words) [view diff] exact match in snippet view article find links to article

derivative a second time, and using the fact that d2 = 0 as well as the linear independence of the εi, the following relations are obtained: d θ j − ∑ i ω i

Normal basis (3,146 words) [view diff] exact match in snippet view article find links to article

normal basis theorem follows from two basic facts. The first is the linear independence of characters: a multiplicative character is a mapping χ from a group

Four exponentials conjecture (2,300 words) [view diff] exact match in snippet view article find links to article

and columns usually means it has rank 2, in this case we require linear independence over a smaller field so the rank isn't forced to be 2. For example

Matrix regularization (2,510 words) [view diff] exact match in snippet view article find links to article

{H_{D}}}:f=h+h';h\in {\mathcal {H_{A}}},h'\in {\mathcal {H_{B}}}} assuming linear independence in A {\displaystyle A} and B {\displaystyle B} . In this case the

Charles Anthony Micchelli (1,598 words) [view diff] exact match in snippet view article find links to article

1137/0730024. Jia, Rong-Qing; Micchelli, Charles A. (1993). "On linear independence for integer translates of a finite number of functions". Proceedings

Cyclic code (5,214 words) [view diff] exact match in snippet view article find links to article

there will be columns who are multiples of each other. So, to get linear independence all non zero m {\displaystyle m} -tuples with one as a top most non

The Vectors of Mind (1,996 words) [view diff] exact match in snippet view article find links to article

definitions are provided for the concepts of trait, ability, test, score, linear independence, statistical independence, experimental independence, reference abilities

Structured sparsity regularization (3,812 words) [view diff] exact match in snippet view article find links to article

H_{A}} , H B {\displaystyle H_{B}} are subspaces. In view of the linear independence assumption, H {\displaystyle H} can be identified with R p + q {\displaystyle

Conformal geometric algebra (3,303 words) [view diff] exact match in snippet view article find links to article

vectors representing points on the object. In the base space, this linear independence manifests as each point lying outside the object defined by the other

Glossary of representation theory (5,011 words) [view diff] exact match in snippet view article find links to article

representation is necessarily cyclic. Dedekind Dedekind's theorem on linear independence of characters. defined over Given a field extension K / F {\displaystyle

Jose Luis Mendoza-Cortes (2,875 words) [view diff] exact match in snippet view article find links to article

establishes a significant connection between these findings and the linear independence of zeta values, leveraging the operad of finite posets to achieve

Poincaré lemma (5,408 words) [view diff] exact match in snippet view article find links to article

does not contain a factor of d x m {\displaystyle dx^{m}} . Due to linear independence of the coordinate differentials, this equation implies that ω ′ =