# 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.

## 16 Citations

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A novel non-convex surrogate that can be optimized by closed-form solutions, such that it empirically converges within dozens of iterations, and which theoretically validate that it is equivalent to the existing matrix completion models.

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This report reports on an implementation of recryption of fully packed ciphertexts using the HElib library for somewhat homomorphic encryption, and includes a much more robust method for deriving the parameters, ensuring that recryption errors only occur with negligible probability.

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This work proposes variations of a Gaussian mixture model (GMM) based channel estimator that was recently proven to be asymptotically optimal in the minimum mean square error (MMSE) sense and argues that these practical baselines are outperformed by far with equal estimation complexity.

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