linear independence
noun
(in linear algebra) the property of a set of elements in a vector space in which none of the vectors can be written as a linear combination of the others.
linearly independent
-
a word derived from
linear independence.
Example Sentences
Examples are provided to illustrate real-world usage of words in context. Any opinions expressed do not reflect the views of Dictionary.com.
If we are able to find two linearly independent solutions to a second-order differential equation, then we can combine them to find the general solution.
From Textbooks ● Mar. 30, 2016
In this case, we know eλx is a solution to Equation 7.1, but it is only one solution and we need two linearly independent solutions to determine the general solution.
From Textbooks ● Mar. 30, 2016
With two exponential functions, unless the exponents are equal, the functions are linearly independent.
From Textbooks ● Mar. 30, 2016
We might be tempted to try a function of the form keλx, where k is some constant, but it would not be linearly independent of eλx.
From Textbooks ● Mar. 30, 2016
The X’s, however, are not necessarily linearly independent.
From Encyclopaedia Britannica, 11th Edition, Volume 12, Slice 6 "Groups, Theory of" to "Gwyniad" by Various
