Högerinvers

Högerinvers is a term used in linear algebra to describe a specific type of inverse matrix. For a given matrix A, a right inverse B is a matrix such that AB = I, where I is the identity matrix. The term "högerinvers" is the Swedish translation of "right inverse." Not all matrices have a right inverse. A matrix A has a right inverse if and only if its columns are linearly independent, which implies that the matrix must be "tall and skinny" (more rows than columns) or square.

If a matrix is square and invertible, its right inverse is unique and is the same as its left inverse (and thus its inverse). However, for non-square matrices, a right inverse, if it exists, is generally not unique. Multiple different matrices B could satisfy AB = I. The existence of a right inverse is related to the concept of the column space of a matrix. If the column space of A spans the entire space of the codomain, then a right inverse exists.

The Moore-Penrose pseudoinverse is a generalized inverse that exists for any matrix and has properties of both left and right inverses. While the standard inverse is unique for invertible square matrices, the existence and uniqueness of a right inverse are conditional on the dimensions and rank of the matrix in question. The study of right inverses is important in solving systems of linear equations, particularly when the system is underdetermined or has infinitely many solutions.