Linear Algebra Find a basis for the solution space of the homogeneous linear system x - y + 2z = 0 2x + y = 0 x - 4y + 6z = 0 How can a basis not be orthogonal? What is a nontrivial relationship linear algebra? How do you find the basis of a polynomial vector space?
In mathematics, a linear equation is defined as a polynomial equation in which the highest exponent of the variables in the equation is 1. These types of equations are called linear, because the graphs of these equations are always lines....
It seems that the first step in this is to construct a “soliton” type localized steady state solution, that is a solution , to the equation that decays in the variable; one can then hope to do a suitable stability (or instability) analysis of this soliton to perturb it to a blowup...
De Broglie, L.: Interpretation of quantum mechanicsby the double solution theory Annales de la Fondation Louis de Broglie, Volume 12,(4) (1987) Couder, Y., Fort, E., Gautier, C.-H., Boudaoud, A.: From Bouncing to Floating: Noncoalescence of Drops on a Fluid Bath. Phys. Rev. Lett...
Being non-commutative, the quaternions do not form a field. However, they are still a skew field (or division ring): multiplication is associative, and every non-zero quaternion has a unique multiplicative inverse. Like the complex numbers, the quaternions have a conjugation although this is...
to the airport by noon. This is a nontrivial challenge on its own. Now imagine you can’t find your glasses (and that you’re as near-sighted as we are). When it comes to solving practical and time-sensitive problems in softwareengineering, observability is a darn good place to start....
Well, the prime application of the Jordan canonical form is to calculate solutions of linear systems of ODEs. The equation with matrix and initial value (both could also be complex). This system has a unique solution which can be given explicitly with the help of the matrix exponential as ...
This is a review of the issue of randomness in quantum mechanics, with special emphasis on its ambiguity; for example, randomness has different antipodal relationships to determinism, computability, and compressibility. Following a (Wittgensteinian) philosophical discussion of randomness in general, I ar...
We argue though that the crucial difference lies not in the non-linearity of the latter, but in the appearance of non-trivial representation theory related to transcendental extensions of the number field which governs the linear solution. An example is studied to illuminate this point....
Well, for funsies, I know of three ways that "infinitessimals" can be made rigorous. One is algebraically; something with a power equal to zero. I...