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 ...
On the -term rank of a matrix 下载积分: 1998 内容提示: Linear Algebra and its Applications 436 (2012) 1632–1643Contents lists available at SciVerse ScienceDirectLinear Algebra and its Applicationsjournal homepage: www.elsevier.com/locate/laaOn the t-term rank of a matrixRichard A. Brualdi...
内容提示: arXiv:1011.5870v1 [math.CO] 26 Nov 2010On the t-Term Rank of a MatrixRichard A. Brualdi, Kathleen P. Kiernan,Seth A. Meyer, Michael W. SchroederDepartment of MathematicsUniversity of WisconsinMadison, WI 53706{brualdi,kiernan,smeyer,schroede}@math.wisc.eduJune 21, 2013Dedicated...
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...
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 ...
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...
For each of the rank(B) linearly independent rows of B, the corresponding component in y can be set to zero or one freely. There are then Ny = 2rank(B) possible vectors y which give solutions to Eq. (1). This means the entanglement entropy between the variable and parity qubits...
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
We obtain an estimate of the maximum value of the minors of the matrix T s,k (n). We find the asymptotic behaviour of the function α A (T s,k (n)) which is equal to the mean value of the square of the minor of rank order of a basis system of rows of the matrix T s,k ...
Rodman, A generalized numerical range: The range of a constrained s... CK Li,PP Mehta,L Rodman - 《Linear & Multilinear Algebra》 被引量: 46发表: 1994年 On the boundary of rank-k numerical ranges rank-knumericalrangeunitdiskUsing the properties of the polynomial p(x, λ) = dWai-Shun...