linear independence

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linear independence

[′lin·ē·ər ‚in·də′pen·dəns]
(mathematics)
The property of a set of vectorsv1,…,vn in a vector space where if a1v1+ a2v2+ … + an vn = 0, then all the scalars ai = 0.
References in periodicals archive ?
The positive slope of the linear dependency of the absolute temperature coefficient of the open-circuit voltage upon the irradiance shows a reduction in voltage drop if the temperature increases when the irradiance increases.
A Gram Schmidt orthonormalization is again performed to avoid numerical errors from linear dependency. A reduced model is defined using the following reduced stiffness and mass matrices
The correlation coefficient r is used for measuring the degree of linear dependency between two variables.
In order to avoid massive numeric operations and transmitting loss, the follow algorithm is used to code and measure linear dependency.
A general family of measures that is not restricted to the case of linear dependency consists of concordance measures.
2006), the critical relative deformations [[epsilon].sub.cr] were determined, below which the quasilinear dependency [sigma] = f ([epsilon]) is maintained and above which a considerable growth of deformations and deviation from linear dependency is observed.
The force model uses a simple linear dependency between the chip thickness and the cutting force.
The shift showed a linear dependency on MWNT content when just the nanocomposites were considered, but an additional extraordinarily large reduction in comparison with PC.
First, linear dependency in the data was removed by fitting an ARMA(1, 0) for the DJIA returns.
Figure 3a and b showed a fair linear regression relationship between TenS and SG ([r.sup.2] = 0.495), but less linear dependency between TenS and ARC ([r.sup.2] = 0.381).
Linear allocation or share systems, because of a budget or other constraint, require that the error terms exhibit linear dependency; this has raised the problem of how to deal, in a symmetric way, with the estimation of parameters in a general linear model (GLM) when the covariance matrix of the error is singular.
showed that the runs up-and-down property of Tausworthe sequences becomes poor when q is small or near to p/2, since two or three tuples of the leading bits of the sequences have linear dependency. This statement is confirmed by the small resolutions in cases where (q, k) = (3, 2) or (13, 3), as shown in Case 2a and d.

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