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Matrix diagonalization is the process of taking a square matrix and converting it into a special type of matrix--a so-called diagonal matrix--that shares the same fundamental ...

Given a matrix A, a Jordan basis satisfies Ab_(i,1)=lambda_ib_(i,1) and Ab_(i,j)=lambda_ib_(i,j)+b_(i,j-1), and provides the means by which any complex matrix A can be ...

Quantifier elimination is the removal of all quantifiers (the universal quantifier forall and existential quantifier exists ) from a quantified system. A first-order theory ...

The Killing form is an inner product on a finite dimensional Lie algebra g defined by B(X,Y)=Tr(ad(X)ad(Y)) (1) in the adjoint representation, where ad(X) is the adjoint ...

The roots of a semisimple Lie algebra g are the Lie algebra weights occurring in its adjoint representation. The set of roots form the root system, and are completely ...

A two-component complex column vector. Spinors can describe both bosons and fermions, while tensors can describe only bosons.

There are two types of singular values, one in the context of elliptic integrals, and the other in linear algebra. For a square matrix A, the square roots of the eigenvalues ...

A root-finding algorithm used in LU decomposition. It solves the N^2 equations i<j l_(i1)u_(1j)+l_(i2)u_(2j)+...+l_(ii)u_(ij)=a_(ij)i=j ...

The cylindrical parts of a system of real algebraic equations and inequalities in variables {x_1,...,x_n} are the terms f_1 <= x_1<=g_1 (1) f_2(x_1) <= x_2<=g_2(x_1) (2) | ...

Eigenvalues are a special set of scalars associated with a linear system of equations (i.e., a matrix equation) that are sometimes also known as characteristic roots, ...