#Wolframalpha vector calculator how to

If you have access to Mathematica, it is more advantageous to use this program than Wolfram Alpha since knowing a programming language is more useful than knowing how to use a. (For instance, you can program MATLAB to find approximate numerical solutions to PDE's. Eigen values and Eigen Vectors were considered for feature extraction stage. Grace Kennedy This is written in a Mathematica notebook since Mathematica is the programming language that powers Wolfram Alpha. This is not really the type of problem that a computer is meant to solve without significant input from the user. Do you expect Wolfram Alpha to tell you, for instance, the spectrum of the Laplace operator on the unit disk? Perhaps if you asked Mathematica to solve a particular PDE with particular boundary conditions, then maybe. Generally a computer algebra system has no way of finding this spectrum. If you are asking about how to compute the spectrum of an operator, then that is a much harder question. (This is a very trivial task since V would be one-dimensional, and so all linear operators are just scalar multiplication.) The Wolfram Language uses state-of-the-art algorithms to bring platform-optimized performance to operations on extremely long, dense, and sparse vectors.

So to make sense of 'eigenvalues of a functional', the functional would have to act on the field F itself, in which case V = F, and the problem is reduced to finding the eigenvalues of a linear operator on a field F. Vectors in the Wolfram Language can always mix numbers and arbitrary symbolic or algebraic elements.

Wolfram Language & System Documentation Center.Do you mean the spectrum of an operator? A functional in this context is a linear map from a vector space V to the field F of scalars.

'Projection.' Wolfram Language & System Documentation Center.

Wolfram Research (2007), Projection, Wolfram Language function, (updated 2014). WolframAlpha can compute these operators along with others, such as the Laplacian, Jacobian and Hessian. Operators such as divergence, gradient and curl can be used to analyze the behavior of scalar- and vector-valued multivariate functions. Cite this as: Wolfram Research (2007), Projection, Wolfram Language function, (updated 2014). Vector analysis is the study of calculus over vector fields.