The Woodbury formula
![(A+UV^(T))^(-1)=A^(-1)-[A^(-1)U(I+V^(T)A^(-1)U)^(-1)V^(T)A^(-1)]](/images/equations/WoodburyFormula/NumberedEquation1.svg) |
is a formula that allows a perturbed matrix to be computed for a change to a given matrix 
, where 
is an identity matrix.
This formula expands the scope of application of the Sherman-Morrison
formula. In particular, in the Woodbury formula, 
and 
can be any (dimensionally compatible) matrices rather than
simple row or column vectors 
and 
for the Sherman-Morrison formula.
