(redirected fromLinearly dependent) Encyclopedia Related to Linearly dependent:Linearly independent 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. ...
Differential Equations determine whether the functions are linearly independent or linearly dependent: y_1 = tan^2 x, y_2 = sec^2 x, y_3 = 1 Solve the linear IVP: xy'+3y=x^2 , y(1)=1. What is y(2)? 1) Solve the IVP: y'' + y' - 2y ...
The Wronskian is a determinant that serves to determine if a set of solutions are linearly dependent or independent; in the first case the result of the Wronskian is zero and in the opposite case, it is different from zero. Ans...
Forum: Linear and Abstract Algebra MHB 12.6 linearly dependent or linearly independent? Are the vectors $$v_1=x^2+1 ,\quad v_2=x+2 ,\quad v_3=x^2+2x$$ linearly dependent or linearly independent? if $$c_1(x^2+1)+c_2(x+2)+c_3(x^2+2x)=0$$ is the system $$\begin{arr...
ait is not difficult to verify that these two functions are linearly independent 核实是不难的这二个作用线性地是独立[translate]
The Wronskian of two functions is found to be zero at x0−ε≤x≤x0+ε for arbitrarily small ε>0. Show that this Wronskian vanishes for all x and that the functions are linearly dependent. 7.6.6 The three functions sin x, ex, and e−x are linearly independent. No one function ...
The solution of the Schrdinger equation HK Ψ = E Ψ is discussed in terms of a basis Φ of n functions of which only p are linearly independent. After introducing a variable ∞ and the matrix K = Φ| H - ∞∞ 1|Φ} = H - ∞δ, a super-secular-equation |K - Δ. 1| = 0...
If a nontrivial solution can be found, then we say that the set of vectors is linearly dependent. If only the trivial solution is satisfied, the set of vectors is said to be linearly independent. To illustrate the case of nontrivial satisfaction of the above equation, let us assume three...
Linearly dependent subspaces and the eigenvalue spectrum of the one-particle reduced density matrix The structure of the one-particle reduced density matrix when expressed in a Cartesian Gaussian basis set is investigated. A set of exact linear dependency... GTSL Schmider - 《Journal of Molecular ...
They introduce also other gates than AND and EXOR to synthesis. I. INTRODUCTION It is known that the Linearly Independent Logic (LI) can create circuits that are superior to AND/EXOR circuits, but there have been no efficient algorithms for the calculation of nonsingular expansions of LI logic...