The possible numbers of zeros in an orthogonal matrix.
The primitive Boolean matrices with the second largest scrambling index by Boolean rank
The scrambling index of an primitive Boolean matrix is the smallest positive integer such that , where denotes the transpose of and denotes the all ones matrix. For an Boolean matrix , its Boolean rank is the smallest positive integer such that for some Boolean matrix and Boolean matrix . In 2009, M. Akelbek, S. Fital, and J. Shen gave an upper bound on the scrambling index of an primitive matrix in terms of its Boolean rank , and they also characterized all primitive...
The principle of truncations in applied probability
The -matrix completion problem.
The q-numerical range of tridiagonal matrices.
The quaternion matrix-valued Young's inequality.
The quaternionic determinant.
The random paving property for uniformly bounded matrices
This note presents a new proof of an important result due to Bourgain and Tzafriri that provides a partial solution to the Kadison-Singer problem. The result shows that every unit-norm matrix whose entries are relatively small in comparison with its dimension can be paved by a partition of constant size. That is, the coordinates can be partitioned into a constant number of blocks so that the restriction of the matrix to each block of coordinates has norm less than one half. The original proof of...
The rank of the difference of similar matrices
The rate of convergence for spectra of GUE and LUE matrix ensembles
We obtain optimal bounds of order O(n −1) for the rate of convergence to the semicircle law and to the Marchenko-Pastur law for the expected spectral distribution functions of random matrices from the GUE and LUE, respectively.
The Rate of Convergence of an Approximate Matrix Factorization Semi-Direct Method.
The rational canonical form of a matrix.
The Rational Invariants of the Tame Quivers.
The real symmetric matrices of odd order with a P-set of maximum size
Suppose that is a real symmetric matrix of order . Denote by the nullity of . For a nonempty subset of , let be the principal submatrix of obtained from by deleting the rows and columns indexed by . When , we call a P-set of . It is known that every P-set of contains at most elements. The graphs of even order for which one can find a matrix attaining this bound are now completely characterized. However, the odd case turned out to be more difficult to tackle. As a first step...
The reciprocal super Catalan matrix
The reciprocal super Catalan matrix has entries [...] . Explicit formulæ for its LU-decomposition, the LU-decomposition of its inverse, and some related matrices are obtained. For all results, q-analogues are also presented.
The Redheffer matrix of a partially ordered set.
The reflexive re-nonnegative definite solution to a quaternion matrix equation.
The relation between Maxwell, Dirac, and the Seiberg-Witten equations.
The relational translators of the hyperspherical functional matrix.
The Re-nonnegative definite solutions to the matrix equation
An complex matrix is called Re-nonnegative definite (Re-nnd) if the real part of is nonnegative for every complex -vector . In this paper criteria for a partitioned matrix to be Re-nnd are given. A necessary and sufficient condition for the existence of and an expression for the Re-nnd solutions of the matrix equation are presented.