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Formalized Mathematics

(a computer assisted approach)

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Volume 15, Issue 3 (Jan 2007)

Issues

The Rank+Nullity Theorem

Jesse Alama
  • Department of Philosophy, Stanford University, USA
Published Online: 2008-06-09 | DOI: https://doi.org/10.2478/v10037-007-0015-6

The Rank+Nullity Theorem

The rank+nullity theorem states that, if T is a linear transformation from a finite-dimensional vector space V to a finite-dimensional vector space W, then dim(V) = rank(T) + nullity(T), where rank(T) = dim(im(T)) and nullity(T) = dim(ker(T)). The proof treated here is standard; see, for example, [14]: take a basis A of ker(T) and extend it to a basis B of V, and then show that dim(im(T)) is equal to |B - A|, and that T is one-to-one on B - A.

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About the article


Published Online: 2008-06-09

Published in Print: 2007-01-01



Citation Information: Formalized Mathematics, ISSN (Online) 1898-9934, ISSN (Print) 1426-2630, DOI: https://doi.org/10.2478/v10037-007-0015-6. Export Citation

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