Rank, Inner Product and Nonsingularity

  • R. B. Bapat
Part of the Universitext book series (UTX)


It is shown that the column rank of a matrix equals its row rank. Basic properties of rank of a product and sum are proved. Inner product is defined and Gram–Schmidt process is described. Orthogonal projection of a vector and orthogonal complement of a subspace are introduced. the rank plus nullity theorem is proved. Various criteria for nonsingularity are given. The Frobenius inequality for rank is proved.


Frobenius Inequality Column Rank Nullity Theorem Pairwise Orthogonal Vectors Fertility Factors 
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Copyright information

© Springer-Verlag London Limited 2012

Authors and Affiliations

  • R. B. Bapat
    • 1
  1. 1.Indian Statistical InstituteNew DelhiIndia

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