The Rank+Nullity Theorem

• Autorzy: Jesse Alama
• Języki publikacji: EN

Abstrakty

EN

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.

• Wydawca: De Gruyter Open
• Czasopismo: Formalized Mathematics
• Rocznik: 2007
• Tom: 15
• Numer: 3
• Strony: 137-142

Daty

wydano

2007-01-01

online

2008-06-09

Twórcy

autor

Jesse Alama

• Department of Philosophy, Stanford University, USA

Bibliografia

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Identyfikatory

DOI

10.2478/v10037-007-0015-6