The identity matrix with an appropriate size is denoted by I. For a complex matrix A, the symbols A∗ and r(A) stand for the conjugate transpose and the rank of A, respectively. The Moore–Penrose inverse of A∈Cm×n, denoted by A†, is defined to be the unique solution X to ...
The problem is considered of finding the nearest rank-deficient matrix to a given rectangular matrix. For a wide class of matrix norms, and arbitrary sparsity imposed on the matrix of perturbations, it is shown that when a solution exists, it can be calculated from the solution of a simpler...
A SURVEY ON RANK AND INERTIA OPTIMIZATION PROBLEMS OF THE MATRIX-VALUED FUNCTION A + BXB~* Numerical Algebra, Control and OptimizationY. TIAN, A survey on rank and inertia optimization problems of the matrix-valued function A + BXB∗ , Numer... YONGGE,TIAN - 《Numerical Algebra Control &...
Based on them, two randomized algorithms are proposed to determine upper and lower bounds for the generic minimum rank of the matrix completions. Our approaches are based on the algebraic geometry theory and the basis preservation principle d...
We consider the problem of finding some structure in the zero-nonzero pattern of a low rank matrix. This problem has strong motivation from theoretical com... P Pudlák - 《Combinatorica》 被引量: 12发表: 2002年 Generalized Eigenvalue Problems for Rectangular Matrices pairwise orthogonalityTwo ...
Matrix Optimization Problem (MOP) A matrix optimization problem (MOP) is defined as follows. Definition 1 Let[Math Processing Error]X∈Rm×nbe a given matrix,[Math Processing Error]ρ:(⋅,⋅)→[0,∞)be a distance/divergence function, and[Math Processing Error]C⊆Rm×n. We say[Math ...
1791Find Center of Star GraphEasySolution.java 1817Finding the Users Active MinutesMediumSolution.java 1829Maximum XOR for Each QueryMediumSolution.java 1971Find if Path Exists in GraphEasySolution.java 2102Sequentially Ordinal Rank TrackerHardSolution.java ...
2387.Median-of-a-Row-Wise-Sorted-Matrix (H-) 3116.Kth-Smallest-Amount-With-Single-Denomination-Combination (H) 3134.Find-the-Median-of-the-Uniqueness-Array (H-) Hash Map 049.Group-Anagrams (M+) 149.Max-Points-on-a-Line (H) 166.Fraction-to-Recurring-Decimal (M) 170.Two-Sum-III-Dat...
The setbeing a basis of, any function therein can be expressed as a linear combination of thes, and this is particularly true with regard to the derivatives. This yields a linear map represented by the infinite-dimensional matrixsuch that ...
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 ...