The nullity and rank of linear combinations of idempotent matrices
نویسندگان
چکیده
منابع مشابه
on the effect of linear & non-linear texts on students comprehension and recalling
چکیده ندارد.
15 صفحه اولRank Nullity Theorem of Linear Algebra
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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In this contribution, we present some formalizations based on the HOL-Multivariate-Analysis session of Isabelle. Firstly, a generalization of several theorems of such library are presented. Secondly, some definitions and proofs involving Linear Algebra and the four fundamental subspaces of a matrix are shown. Finally, we present a proof of the result known in Linear Algebra as the “Rank-Nullity...
متن کاملNotes on linear combinations of two tripotent , idempotent , and involutive matrices that commute
The aim of this paper is to provide alternate proofs of all the results of our previous paper [2] in the particular case when the given two matrices A1 and A2 in the linear combination A = c1A1 + c2A2 commute.
متن کاملRank of convex combinations of matrices
where T and S are diagonal m.by.m and n-by-n real matrices, respectively with diagonal entries from [0, 1]. Our goal is to characterize the above sets with respect to the inheri tance of rank r , which is meant that each matr ix f rom these sets is of rank r . It should b e noted that, for square and nonsingular A and B, nonsingulari ty o f our sets has been studied in [2]. We shall dose this s...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2006
ISSN: 0024-3795
DOI: 10.1016/j.laa.2006.01.011