• On the Rank of a Matrix

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      Permanent link:
      https://www.ias.ac.in/article/fulltext/reso/026/04/0575-0578

    • Keywords

       

      Rank of a matrix, range of a linear operator, Fredh¨olm alternative, rank-nullity theorem.

    • Abstract

       

      Two important results in linear algebra are the ‘rank-nullity theorem’ and the equality of the row and column ranks of a matrix. In this note, we will give a simple proof of the latter, using the former. As a by-product, we also prove the Fredholm alternative, which characterizes the range of the linear operator associated with a matrix.

    • Author Affiliations

       

      S Kesavan1

      1. Adjunct Faculty Department of Mathematics Indian Institute of Technology-Madras IIT P.O., Chennai 600 036
    • Dates

       

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