Relationship between the Inverses of a Matrix and a Submatrix

@article{Ruiz2016RelationshipBT,
  title={Relationship between the Inverses of a Matrix and a Submatrix},
  author={E. Ju{\'a}rez Ruiz and R. Cortes Maldonado and F. P{\'e}rez Rodr{\'i}guez},
  journal={Computaci{\'o}n y Sistemas},
  year={2016},
  volume={20}
}
A simple and straightforward formula for computing the inverse of a submatrix in terms of the inverse of the original matrix is derived. General formulas for the inverse of submatrices of order 𝑛 − 𝑘 as well as block submatrices are derived. The number of additions (or subtractions) and multiplications (or divisions) on the formula is calculated. A variety of numerical results are shown. 
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