Two important results in linear algebra are the 'rank-nullity theorem' and the equality of the row and column ranks of a matrix. In this note, we will give a simple proof of the latter, using the former. As a by-product, we also prove the Fredhlm alternative, which characterizes the ...
Let A be the incidence matrix of a block design constructed from a relative difference set. Let r p be the rank mod p of A where p is a prime. In this paper we find inequalities for r p and determine r p completely in some cases, in particular when A is the incidence matrix of ...
H.M. Möller improved the lower bound for the number of nodes in odd degree cubature formulae by an additional term. This term is the rank of a matrix depending on the moments of the integral considered. For the integrals in question the determination of this matrix and the computation of...
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accepted manuscript the geometry of rank decompositions of matrix multiplication ii: 3 × 3 matrices the geometry of rank decompositions of matrix multipli... This is the second in a series of papers on rank decompositions of the matrix multiplication tensor. We present new rank 23 decompositions...
Matrix Rank Calculator Find the rank of a matrix quickly and easily, using our rank calculator. With support for matrices of up to 6x6 size, you can solve most problems in seconds. Matrix Power Calculator Calculate the power of a matrix easily, using our powerful matrix power calculator. With...
Structure ranks of matrices The structure rank of a matrix, i.e. the maximum order of a nonsingular submatrix all of whose entries are located in a given structure (a subset of M 脳 ... M Fiedler - 《Linear Algebra & Its Applications》 被引量: 53发表: 1993年 More on structure-ranks...
ω. These include Pan’s Trilinear Aggregation, Bini’s Border Rank and Sch¨onhage’s Asymptotic Sum inequality. In chapter 2, we look in detail at the current best estimate of ω found by Copper- smith and Winograd. We also propose a different method of evaluating the “value” of ...
On the rank of payoff matrices with long-term assets We exhibit a sufficient condition under which the payoff matrix and the full payoff matrix have the same rank. This generalizes previous results of Angeloni-Cornet and Magill-Quinzii involving only short-term assets. We then derive ... JM...
作者: A Sen 摘要: Consider the matrix Δ n =(( I(X i +X j >0) )) i,j=1,2,...,n where {X i } are i.i.d.\ and their distribution is continuous and symmetric around 0 . We show that the rank r n of this matrix is equal in distribution to 2∑ n−1 i=1 I(ξ ...