<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>1405-5546</journal-id>
<journal-title><![CDATA[Computación y Sistemas]]></journal-title>
<abbrev-journal-title><![CDATA[Comp. y Sist.]]></abbrev-journal-title>
<issn>1405-5546</issn>
<publisher>
<publisher-name><![CDATA[Instituto Politécnico Nacional, Centro de Investigación en Computación]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S1405-55462016000200251</article-id>
<article-id pub-id-type="doi">10.13053/cys-20-2-2083</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Relationship between the Inverses of a Matrix and a Submatrix]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Juárez-Ruiz]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Cortés-Maldonado]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Pérez-Rodríguez]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Benemérita Universidad Autónoma de Puebla Facultad de Ciencias de la Electrónica ]]></institution>
<addr-line><![CDATA[ Puebla]]></addr-line>
<country>Mexico</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Benemérita Universidad Autónoma de Puebla Instituto de Física ]]></institution>
<addr-line><![CDATA[ Puebla]]></addr-line>
<country>Mexico</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>06</month>
<year>2016</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>06</month>
<year>2016</year>
</pub-date>
<volume>20</volume>
<numero>2</numero>
<fpage>251</fpage>
<lpage>262</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S1405-55462016000200251&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S1405-55462016000200251&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S1405-55462016000200251&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract 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.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Matrix inverse]]></kwd>
<kwd lng="en"><![CDATA[submatrix]]></kwd>
<kwd lng="en"><![CDATA[discrete Fourier transform]]></kwd>
</kwd-group>
</article-meta>
</front><back>
<ref-list>
<ref id="B1">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[Fast exact linear and non-linear structural reanalysis and the Sherman-Morrison-Woodbury formulas]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Akgün]]></surname>
<given-names><![CDATA[M.A.]]></given-names>
</name>
<name>
<surname><![CDATA[Garcelon]]></surname>
<given-names><![CDATA[J.H.]]></given-names>
</name>
<name>
<surname><![CDATA[Haftka]]></surname>
<given-names><![CDATA[R.T.]]></given-names>
</name>
</person-group>
<source><![CDATA[International Journal for Numerical Methods in Engineering]]></source>
<year>2001</year>
<volume>50</volume>
<numero>7</numero>
<issue>7</issue>
<page-range>15871606</page-range></nlm-citation>
</ref>
<ref id="B2">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Allaire]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
<name>
<surname><![CDATA[Kaber]]></surname>
<given-names><![CDATA[S.M.]]></given-names>
</name>
</person-group>
<source><![CDATA[Numerical linear algebra]]></source>
<year>2008</year>
<volume>55</volume>
<publisher-loc><![CDATA[New York ]]></publisher-loc>
<publisher-name><![CDATA[Springer]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B3">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Alshehri]]></surname>
<given-names><![CDATA[K.M.A.]]></given-names>
</name>
</person-group>
<source><![CDATA[Multi-period demand response management in the smart grid: a Stackelberg game approach]]></source>
<year>2015</year>
</nlm-citation>
</ref>
<ref id="B4">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[Perturbed matrix inversion with application to LP simplex method]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Arsham]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
<name>
<surname><![CDATA[Grad]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Jaklic]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
</person-group>
<source><![CDATA[Applied mathematics and computation]]></source>
<year>2007</year>
<volume>188</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>801-7</page-range></nlm-citation>
</ref>
<ref id="B5">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[An inverse matrix adjustment arising in discriminant analysis]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Bartlett]]></surname>
<given-names><![CDATA[M.S.]]></given-names>
</name>
</person-group>
<source><![CDATA[The Annals of Mathematical Statistics]]></source>
<year>1951</year>
<volume>22</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>107-11</page-range></nlm-citation>
</ref>
<ref id="B6">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Birkhoff]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
<name>
<surname><![CDATA[Mac Lane]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
</person-group>
<source><![CDATA[A survey of modern algebra]]></source>
<year>1965</year>
<publisher-name><![CDATA[Universities Press]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B7">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[Preconditioning Sparse Nonsymmetric Linear Systems with the Sherman--Morrison Formula]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Bru]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
<name>
<surname><![CDATA[Cerdán]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Marín]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Mas]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<source><![CDATA[SIAM Journal on Scientific Computing]]></source>
<year>2003</year>
<volume>25</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>701-15</page-range></nlm-citation>
</ref>
<ref id="B8">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[Anisotropy effects in homogenized magneto-dielectric photonic crystals]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Cerdán-Ramírez]]></surname>
<given-names><![CDATA[V.]]></given-names>
</name>
<name>
<surname><![CDATA[Zenteno-Mateo]]></surname>
<given-names><![CDATA[B.]]></given-names>
</name>
<name>
<surname><![CDATA[Sampedro]]></surname>
<given-names><![CDATA[M.P.]]></given-names>
</name>
<name>
<surname><![CDATA[Palomino-Ovando]]></surname>
<given-names><![CDATA[M.A.]]></given-names>
</name>
<name>
<surname><![CDATA[Flores-Desirena]]></surname>
<given-names><![CDATA[B.]]></given-names>
</name>
<name>
<surname><![CDATA[Pérez-Rodríguez]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
</person-group>
<source><![CDATA[Journal of Applied Physics]]></source>
<year>2009</year>
<volume>106</volume>
<numero>10</numero>
<issue>10</issue>
</nlm-citation>
</ref>
<ref id="B9">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[Matrix Inverse as by-Product of Determinant]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Chang]]></surname>
<given-names><![CDATA[F.C.]]></given-names>
</name>
</person-group>
<source><![CDATA[British Journal of Mathematics &amp; Computer Science]]></source>
<year>2016</year>
<volume>12</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>1</page-range></nlm-citation>
</ref>
<ref id="B10">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[Matrix inversion by rank annihilation]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Edelblute]]></surname>
<given-names><![CDATA[D.J.]]></given-names>
</name>
</person-group>
<source><![CDATA[Mathematics of Computation]]></source>
<year>1966</year>
<volume>20</volume>
<numero>93</numero>
<issue>93</issue>
<page-range>149-51</page-range></nlm-citation>
</ref>
<ref id="B11">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[Explicit inverse of a generalized Vandermonde matrix]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[El-Mikkawy]]></surname>
<given-names><![CDATA[M.E.]]></given-names>
</name>
</person-group>
<source><![CDATA[Applied mathematics and computation]]></source>
<year>2003</year>
<volume>146</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>643-51</page-range></nlm-citation>
</ref>
<ref id="B12">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Golub]]></surname>
<given-names><![CDATA[G.H.]]></given-names>
</name>
<name>
<surname><![CDATA[Van Loan]]></surname>
<given-names><![CDATA[C.F.]]></given-names>
</name>
</person-group>
<source><![CDATA[Matrix computations]]></source>
<year>2012</year>
<volume>3</volume>
<publisher-name><![CDATA[JHU Press]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B13">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[Enlargement methods for computing the inverse matrix]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Guttman]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
</person-group>
<source><![CDATA[The Annals of Mathematical Statistics]]></source>
<year>1946</year>
<volume>17</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>335-43</page-range></nlm-citation>
</ref>
<ref id="B14">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[Updating the inverse of a matrix]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Hager]]></surname>
<given-names><![CDATA[W.W.]]></given-names>
</name>
</person-group>
<source><![CDATA[SIAM Rev.]]></source>
<year>1989</year>
<volume>31</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>221-39</page-range></nlm-citation>
</ref>
<ref id="B15">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[Early experience with the Intel iPSC/860 at Oak Ridge National Laboratory]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Heath]]></surname>
<given-names><![CDATA[M.T.]]></given-names>
</name>
<name>
<surname><![CDATA[Geist]]></surname>
<given-names><![CDATA[G.A.]]></given-names>
</name>
<name>
<surname><![CDATA[Drake]]></surname>
<given-names><![CDATA[J.B.]]></given-names>
</name>
</person-group>
<source><![CDATA[International Journal of High Performance Computing Applications]]></source>
<year>1991</year>
<volume>5</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>10-26</page-range></nlm-citation>
</ref>
<ref id="B16">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[On deriving the inverse of a sum of matrices]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Henderson]]></surname>
<given-names><![CDATA[H.V.]]></given-names>
</name>
<name>
<surname><![CDATA[Searle]]></surname>
<given-names><![CDATA[S.R.]]></given-names>
</name>
</person-group>
<source><![CDATA[SIAM Rev.]]></source>
<year>1981</year>
<volume>23</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>53-60</page-range></nlm-citation>
</ref>
<ref id="B17">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Higham]]></surname>
<given-names><![CDATA[N.]]></given-names>
</name>
</person-group>
<source><![CDATA[Accuracy and Stability of Numerical Algorithms]]></source>
<year>1996</year>
<page-range>203-6</page-range><publisher-name><![CDATA[SIAM]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B18">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[The solution of linear systems by using the Sherman-Morrison formula]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Maponi]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
</person-group>
<source><![CDATA[Linear Algebra and its Applications]]></source>
<year>2007</year>
<volume>420</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>276-94</page-range></nlm-citation>
</ref>
<ref id="B19">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[On the inverse of the sum of matrices]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Miller]]></surname>
<given-names><![CDATA[K.S.]]></given-names>
</name>
</person-group>
<source><![CDATA[Mathematics Magazine]]></source>
<year>1981</year>
<volume>54</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>67-72</page-range></nlm-citation>
</ref>
<ref id="B20">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Press]]></surname>
<given-names><![CDATA[W.H.]]></given-names>
</name>
<name>
<surname><![CDATA[Teukolsky]]></surname>
<given-names><![CDATA[S.A.]]></given-names>
</name>
<name>
<surname><![CDATA[Vetterling]]></surname>
<given-names><![CDATA[W.T.]]></given-names>
</name>
<name>
<surname><![CDATA[Flannery]]></surname>
<given-names><![CDATA[B.P.]]></given-names>
</name>
</person-group>
<source><![CDATA[Numerical Recipes in Fortran 90: The Art of Parallel Scientific Computing]]></source>
<year>1996</year>
<publisher-name><![CDATA[Cambridge University Press]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B21">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[From photonic crystals to metamaterials: the bianisotropic response]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Reyes-Avendaño]]></surname>
<given-names><![CDATA[J.A.]]></given-names>
</name>
<name>
<surname><![CDATA[Algredo-Badillo]]></surname>
<given-names><![CDATA[U.]]></given-names>
</name>
<name>
<surname><![CDATA[Halevi]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
<name>
<surname><![CDATA[Pérez-Rodríguez]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
</person-group>
<source><![CDATA[New Journal of Physics]]></source>
<year>2011</year>
<volume>13</volume>
<numero>7</numero>
<issue>7</issue>
</nlm-citation>
</ref>
<ref id="B22">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[Bianisotropic metamaterials based on twisted asymmetric crosses]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Reyes-Avendaño]]></surname>
<given-names><![CDATA[J.A.]]></given-names>
</name>
<name>
<surname><![CDATA[Sampedro]]></surname>
<given-names><![CDATA[M. P.]]></given-names>
</name>
<name>
<surname><![CDATA[Juárez-Ruiz]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
<name>
<surname><![CDATA[Pérez-Rodríguez]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
</person-group>
<source><![CDATA[Journal of Optics]]></source>
<year>2014</year>
<volume>16</volume>
<numero>6</numero>
<issue>6</issue>
</nlm-citation>
</ref>
<ref id="B23">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[Adjustment of an inverse matrix corresponding to a change in one element of a given matrix]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Sherman]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Morrison]]></surname>
<given-names><![CDATA[W.J.]]></given-names>
</name>
</person-group>
<source><![CDATA[The Annals of Mathematical Statistics]]></source>
<year>1950</year>
<volume>21</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>124-7</page-range></nlm-citation>
</ref>
<ref id="B24">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[Matrix inversion by the annihilation of rank]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Wilf]]></surname>
<given-names><![CDATA[H.S.]]></given-names>
</name>
</person-group>
<source><![CDATA[Journal of the Society for Industrial and Applied Mathematics]]></source>
<year>1959</year>
<volume>7</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>149-51</page-range></nlm-citation>
</ref>
<ref id="B25">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[Effective permittivity tensor for a metal-dielectric superlattice]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Zenteno-Mateo]]></surname>
<given-names><![CDATA[B.]]></given-names>
</name>
<name>
<surname><![CDATA[Cerdan-Ramirez]]></surname>
<given-names><![CDATA[V.]]></given-names>
</name>
<name>
<surname><![CDATA[Flores-Desirena]]></surname>
<given-names><![CDATA[B.]]></given-names>
</name>
<name>
<surname><![CDATA[Sampedro]]></surname>
<given-names><![CDATA[M. P.]]></given-names>
</name>
<name>
<surname><![CDATA[Juarez-Ruiz]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
<name>
<surname><![CDATA[Perez-Rodriguez]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
</person-group>
<source><![CDATA[Progress in Electromagnetic Research Letters]]></source>
<year>2011</year>
<volume>22</volume>
<page-range>165-74</page-range></nlm-citation>
</ref>
</ref-list>
</back>
</article>
