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 Eigen  3.3.90 (git rev e4b24e7fb24c280e1db096edd983ee29e255e3b8)
Dense linear problems and decompositions

## Modules

Linear algebra and decompositions
This page explains how to solve linear systems, compute various decompositions such as LU, QR, SVD, eigendecompositions... After reading this page, don't miss our catalogue of dense matrix decompositions.

Catalogue of dense decompositions
This page presents a catalogue of the dense matrix decompositions offered by Eigen. For an introduction on linear solvers and decompositions, check this page . To get an overview of the true relative speed of the different decompositions, check this benchmark .

Solving linear least squares systems
This page describes how to solve linear least squares systems using Eigen. An overdetermined system of equations, say Ax = b, has no solutions. In this case, it makes sense to search for the vector x which is closest to being a solution, in the sense that the difference Ax - b is as small as possible. This x is called the least square solution (if the Euclidean norm is used).

Inplace matrix decompositions
Starting from Eigen 3.3, the LU, Cholesky, and QR decompositions can operate inplace, that is, directly within the given input matrix. This feature is especially useful when dealing with huge matrices, and or when the available memory is very limited (embedded systems).

Benchmark of dense decompositions
This page presents a speed comparison of the dense matrix decompositions offered by Eigen for a wide range of square matrices and overconstrained problems.

Reference