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# Jacobi eigenvalue algorithm

In numerical linear algebra, the Jacobi eigenvalue algorithm is an iterative method for the calculation of the eigenvalues and eigenvectors of a real symmetric matrix (a process known as diagonalization). [1]

## Arnold Schönhage

Arnold Schönhage (born 1 December 1934 in Lockhausen, now Bad Salzuflen, Free State of Lippe) is a German mathematician and computer scientist.

## Carl Gustav Jacob Jacobi

Carl Gustav Jacob Jacobi (10 December 1804 – 18 February 1851) was a German mathematician, who made fundamental contributions to elliptic functions, dynamics, differential equations, and number theory.

## Crelle's Journal

Crelle's Journal, or just Crelle, is the common name for a mathematics journal, the Journal für die reine und angewandte Mathematik (in English: Journal for Pure and Applied Mathematics).

## Diagonal

In geometry, a diagonal is a line segment joining two vertices of a polygon or polyhedron, when those vertices are not on the same edge.

## Eigenvalues and eigenvectors

In linear algebra, an eigenvector or characteristic vector of a linear transformation is a non-zero vector that changes by only a scalar factor when that linear transformation is applied to it.

## Givens rotation

In numerical linear algebra, a Givens rotation is a rotation in the plane spanned by two coordinates axes.

## Hilbert matrix

In linear algebra, a Hilbert matrix, introduced by, is a square matrix with entries being the unit fractions For example, this is the 5 &times; 5 Hilbert matrix: 1 & \frac & \frac & \frac & \frac \\ \frac & \frac & \frac & \frac & \frac \\ \frac & \frac & \frac & \frac & \frac \\ \frac & \frac & \frac & \frac & \frac \\ \frac & \frac & \frac & \frac & \frac \end.

## Iterative method

In computational mathematics, an iterative method is a mathematical procedure that uses an initial guess to generate a sequence of improving approximate solutions for a class of problems, in which the n-th approximation is derived from the previous ones.

## Jacobi method for complex Hermitian matrices

In mathematics, the Jacobi method for complex Hermitian matrices is a generalization of the Jacobi iteration method.

## Jacobi rotation

In numerical linear algebra, a Jacobi rotation is a rotation, Qkℓ, of a 2-dimensional linear subspace of an n-dimensional inner product space, chosen to zero a symmetric pair of off-diagonal entries of an n×n real symmetric matrix, A, when applied as a similarity transformation: \begin \end \to \begin \end.

## Mathematics of Computation

Mathematics of Computation is a bimonthly mathematics journal focused on computational mathematics.

## Matrix norm

In mathematics, a matrix norm is a vector norm in a vector space whose elements (vectors) are matrices (of given dimensions).

## Matrix similarity

In linear algebra, two n-by-n matrices and are called similar if for some invertible n-by-n matrix.

## Numerical linear algebra

Numerical linear algebra is the study of algorithms for performing linear algebra computations, most notably matrix operations, on computers.

## Real number

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.

## Round-off error

A round-off error, also called rounding error, is the difference between the calculated approximation of a number and its exact mathematical value due to rounding.

## Symmetric matrix

In linear algebra, a symmetric matrix is a square matrix that is equal to its transpose.

## References

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