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- Constrained_generalized_inverse abstract "In linear algebra, a constrained generalized inverse is obtained by solving a system of linear equations with an additional constraint that the solution is in a given subspace. One also says that the problem is described by a system of constrained linear equations.In many practical problems, the solution of a linear system of equationsis acceptable only when it is in a certain linear subspace of .In the following, the orthogonal projection on will be denoted by .Constrained system of linear equationshas a solution if and only if the unconstrained system of equations is solvable. If the subspace is a proper subspace of , then the matrix of the unconstrained problem may be singular even if the system matrix of the constrained problem is invertible (in that case, ). This means that one needs to use a generalized inverse for the solution of the constrained problem. So, a generalized inverse of is also called a -constrained pseudoinverse of . An example of a pseudoinverse that can be used for the solution of a constrained problem is the Bott-Duffin inverse of constrained to , which is defined by the equationif the inverse on the right-hand-side exists.".
- Constrained_generalized_inverse wikiPageID "16817400".
- Constrained_generalized_inverse wikiPageRevisionID "556596068".
- Constrained_generalized_inverse hasPhotoCollection Constrained_generalized_inverse.
- Constrained_generalized_inverse subject Category:Matrices.
- Constrained_generalized_inverse type Abstraction100002137.
- Constrained_generalized_inverse type Arrangement107938773.
- Constrained_generalized_inverse type Array107939382.
- Constrained_generalized_inverse type Group100031264.
- Constrained_generalized_inverse type Matrices.
- Constrained_generalized_inverse type Matrix108267640.
- Constrained_generalized_inverse comment "In linear algebra, a constrained generalized inverse is obtained by solving a system of linear equations with an additional constraint that the solution is in a given subspace.".
- Constrained_generalized_inverse label "Constrained generalized inverse".
- Constrained_generalized_inverse sameAs m.04079c0.
- Constrained_generalized_inverse sameAs Q5164361.
- Constrained_generalized_inverse sameAs Q5164361.
- Constrained_generalized_inverse sameAs Constrained_generalized_inverse.
- Constrained_generalized_inverse wasDerivedFrom Constrained_generalized_inverse?oldid=556596068.
- Constrained_generalized_inverse isPrimaryTopicOf Constrained_generalized_inverse.