A note on the nullity theorem
نویسندگان
چکیده
منابع مشابه
A short note on the nullity theorem
In this paper we take a close look at the nullity theorem as formulated by Markham and Fiedler in 1986. The theorem is a valuable tool in the computations with structured rank matrices, it connects ranks of subblocks of an invertible matrix A with ranks of other subblocks in his inverse A. A little earlier, Barrett and Feinsilver, 1981, proved a theorem very close to the nullity theorem, but re...
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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...
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In this article we present a proof of the result known in Linear Algebra as the “rank nullity Theorem”, which states that, given any linear form f from a finite dimensional vector space V to a vector space W , then the dimension of V is equal to the dimension of the kernel of f (which is a subspace of V ) and the dimension of the range of f (which is a subspace of W ). The proof presented here ...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2006
ISSN: 0377-0427
DOI: 10.1016/j.cam.2005.02.007