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Any square matrix T has a canonical form without any need to extend the field of its coefficients. For instance, if the entries of T are rational numbers, then so are the ...

The Sobolev embedding theorem is a result in functional analysis which proves that certain Sobolev spaces W^(k,p)(Omega) can be embedded in various spaces including ...

The conjugate gradient method can be viewed as a special variant of the Lanczos method for positive definite symmetric systems. The minimal residual method and symmetric LQ ...

Analytic number theory is the branch of number theory which uses real and complex analysis to investigate various properties of integers and prime numbers. Examples of topics ...

The angle of attack alpha of a surface is measured as the angle between the direction of fluid flow relative to the surface, and the line in the direction of normal fluid ...

For a curve with first fundamental form ds^2=Edu^2+2Fdudv+Gdv^2, (1) the Gaussian curvature is K=(M_1-M_2)/((EG-F^2)^2), (2) where M_1 = |-1/2E_(vv)+F_(uv)-1/2G_(uu) 1/2E_u ...

A derivative of a complex function, which must satisfy the Cauchy-Riemann equations in order to be complex differentiable.

Given a differential operator D on the space of differential forms, an eigenform is a form alpha such that Dalpha=lambdaalpha (1) for some constant lambda. For example, on ...

If L^~ is a linear operator on a function space, then f is an eigenfunction for L^~ and lambda is the associated eigenvalue whenever L^~f=lambdaf. Renteln and Dundes (2005) ...

If A is an n×n square matrix and lambda is an eigenvalue of A, then the union of the zero vector 0 and the set of all eigenvectors corresponding to eigenvalues lambda is ...