The operator which best approximates a solution to a linear system with a singular (non-invertible) matrix.: e.g., the Moore-Penrose pseudoinverse. Use when a question concerns a matrix that is probably singular.
This tag applies to, but is not restricted to:
Moore-Penrose Pseudoinverse
(also "Generalized Inverse") For linear operators and matrices that are not invertible there still exists a unique Moore-Penrose Pseudoinverse $A^+$ which fulfils the following conditions:
- $A A^+A = A$ ($AA^+$ need not be the general identity matrix, but it maps all column vectors of $A$ to themselves);
- $A^+A A^+ = A^+$ ($A^+$ is a weak inverse for the multiplicative semigroup);
- $(AA^+)^* = AA^+$ ($AA^+$ is Hermitian); and
- $(A^+A)^* = A^+A$ ($A^+A$ is also Hermitian).
Use it: when the Matrix/Operator involved is (probably) singular
Don't use it: when the Matrix/Operator is definitely invertible or its state is unknown
