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.
Constrained system of linear equations has a solution if and only if the unconstrained system of equations is solvable.
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.
An example of a pseudoinverse that can be used for the solution of a constrained problem is the Bott–Duffin inverse of
, which is defined by the equation if the inverse on the right-hand-side exists.
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