Weak vs Strong Dependency - Mathematics Stack Exchange In probability, weak dependence of random variables is a generalization of independence that is weaker than the concept of a martingale A (time) sequence of random variables is weakly dependent if distinct portions of the sequence have a covariance that asymptotically decreases to 0 as the blocks are further separated in time
Linear Dependence Lemma - Mathematics Stack Exchange This is out of my textbook, Axler's "Linear Algebra Done Right" which I am self-studying from (I organized my thoughts in which I would like some sort of response with Roman Numerals) Linear
What exactly does linear dependence and linear independence imply . . . Mathematical Definition of Linear Dependence Let S be the set of vectors S = {V1, V2, V3,… ,Vn} The set S is linearly dependent if and only if CV1+ C2V2 + C3V3 +… + CnVn=zero vector for some all Ci’s at least one is non zero The condition of checking linear dependence if c1 or c2 is non zero then the two vectors are linearly dependent
partial differential equations - Continuous dependence on parameters . . . "Linear PDEs" is already a very large class, but if you restrict to a well-understood class of problems with established estimates then you can often get as-smooth-as-possible dependence on the coefficients Here's a very rough sketch of how to proceed for a simple example:
Continuous dependence of solutions to ODEs on parameters Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers
Is there a symbol for dependent? - Mathematics Stack Exchange This is an accurate example of a text using a symbol for dependence, exactly what the questioner wanted! Came here because I'm reading it and looking for the latex $\endgroup$ – Joseph Garvin
Is there such a thing as quadratic independence (and higher . . . There is also a general concept of dependence relations which includes linear dependence and algebraic dependence as special cases Haven't searched online but you can find it in N Jacobson, Basic Algebra vol II, section 3 6