linear independence

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linear independence

n.
The property of a set of vectors of having no linear combinations equal to zero unless all of the coefficients are equal to zero.
American Heritage® Dictionary of the English Language, Fifth Edition. Copyright © 2016 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.
References in periodicals archive ?
Let x and y be linearly independent unit vectors in our Hubert space and P and Q the projections onto the subspaces they generate.
We provide an algorithm in terms of linear algebra to determine whether or not H is nondegenerate over F: For any hyperplane H [subset] [P.sup.n](F) with coefficients in F; Let L be the linear form in n+1 variables defining H, that is [Mathematical Expressions Omitted], where P is the projection map; For , a set of linear forms in n+1 variables which are pairwise linearly independent, we denote by [(L).sub.F] the vector space generated by the linear forms in L over F.
Both (2) and (3) comprise N x [N.sub.j] linearly independent, non-homogeneous equations for the [N.sub.j] firms in N industries and have, therefore, unique solutions.
Once the ciphertexts of 2n linearly independent message vectors are known, the encryption function is uniquely defined.
These packets, which are defined over [F.sup.n.sub.q], arrive at the sink nodes where they must be linearly independent so that the system has a solution.
Suppose that the set L([[alpha].sub.1], ..., [[alpha].sub.n]) is linearly independent over the field of rational numbers Q, and [c.sub.1], ..., [c.sub.n] are complex numbers, at least one of them is non-zero.
Also three linearly independent solutions of the field equations in (1), namely, of the system of equations (9), are given by
The new training data subset is generated by the linearly independent base transformation.
Firstly, we will show that S is a linearly independent subset of H [union] {0}.
Notice that the geometric multiplicity is the largest number of linearly independent eigenvectors associated with an eigenvalue.
Second calculate the all-possible paths of the TFG based on formula which is the possible paths equal the number of linearly independent paths.
The hyperplanes [H.sub.1], ..., [H.sub.k] in A are linearly independent if their normals are linearly independent.
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