Core-EP decomposition and its applications
Keywords: 15A09; 15A57; 15A24Core-EP decomposition; Core-EP inverse; Core-EP order; Core-minus partial order
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The Bott–Duffin (e,f)-inverses and their applications
Keywords: 15A09; 16U99; 16S50Generalized inverse; Bott–Duffin (e,f)(e,f)-inverse; Outer generalized inverse; Image-kernel (p,q)(p,q)-inverse
On the Drazin inverse of an anti-triangular block matrix
Keywords: 15A09; 47A05Operator equation; Drazin inverse; Group inverse; Block matrix
Lower triangular Toeplitz–Ramanujan systems whose solution yields the Bernoulli numbers
Keywords: 11B68; 11Y55; 15A06; 15A09; 15A24; 15B05; 15B99; 65F05Bernoulli numbers; Triangular Toeplitz matrices
Neural network approach to computing outer inverses based on the full rank representation
Keywords: 15A09; 15A23; 68T05Generalized inverse AT,S(2); Recurrent neural network; Dynamical system; Matrix spectrum
Applications of Riordan matrix functions to Bernoulli and Euler polynomials
Keywords: 05A05; 05A15; 15B36; 15A09; 05A30; 05A10; 05A19Riordan array; Riordan group; Pascal matrix; Bernoulli polynomials and numbers; Euler polynomials and numbers; Conjugate Bernoulli and Euler polynomials
Multiplicative perturbation theory of the Moore–Penrose inverse and the least squares problem
Keywords: 15A09; 15A12; 65F35Least squares problems; Moore–Penrose inverse; Multiplicative perturbation theory
LU factorization for matrices in quasiseparable form via orthogonal transformations
Keywords: 15A09; 15A23; 65F05Structured matrix; Quasiseparable representations; Fast algorithms; LU factorization
The Hermitian solution of AXA*=B subject to CXC* ⥠D
Keywords: 15A09; 15A24; 15A39; Hermitian solution; Linear matrix equation; Linear matrix inequality; Löwner partial ordering;
Green matrices associated with generalized linear polyominoes
Keywords: 15A09; 39A05; Polyominoes; Green matrices; Green function; Effective resistance; Kirchhoff index;
Characterizations and representations of the (P, Q)-outer generalized inverse
Keywords: (P, Q)-outer generalized inverse; Idempotent; Orthogonal projector; Positive operator; Moore Penrose inverse; Drazin inverse; 15A09; 47A05;
Solution to a system of real quaternion matrix equations encompassing η-Hermicity
Keywords: Linear matrix equation; η-Hermitian solution; Quaternion matrix; Moore–Penrose inverse; Rank; General solution15A24; 15A09; 11R52; 15B57
Weighted partial isometries and weighted-EP elements in C*-algebras
Keywords: Weighted-EP elements; Moore–Penrose inverse; Group inverse; C*-algebra46L05; 47A05; 15A09
Expressions for the Moore–Penrose inverse of block matrices involving the Schur complement
Keywords: 15A09; 15A03; 65F20Moore–Penrose inverse; Block matrix; Schur complement; Bordered matrix
Several Anzahl theorems of matrices over Galois rings and their applications
Keywords: 05B20; 05E30; 34A30; 15A09; Galois ring; Orbit; Association scheme; System of linear equations; Generalized invertible matrix; Idempotent matrix; Involutory matrix;
Partial orders on B(H)
Keywords: 15A09; 47A05; 47A99; Minus partial order; Star partial order; Sharp partial order; Core partial order;
The Moore–Penrose inverses of matrices over quaternion polynomial rings
Keywords: 15A09; 68W30Quaternion polynomial matrix; Moore–Penrose inverse; Leverrier–Faddeev algorithm
Applications of completions of operator matrices to reverse order law for {1}-inverses of operators on Hilbert spaces
Keywords: 47A05; 15A09; Generalized inverse; {1}-inverses; Completions of operator matrices; Reverse order law;
The conservative system of N atoms coupled with one photon
Keywords: 11C20; 11D72; 15A06; 15A09; 44A10; 45A05; 45F05; 45F15; Many-body solution; Weisskopf-Wigner; Markovian; Collective; Absorption;
Partial orders in rings based on generalized inverses – unified theory
Keywords: 06A06; 15A09; 16U99Matrix partial ordering; GG-based order relation; Minus partial order; Star partial order; Sharp partial order; Core partial order; Generalized inverse; Moore–Penrose inverse; Group inverse; Core inverse; Ring; Dedekind finite ring
Inverse invariant zero-nonzero patterns
Keywords: 15A09; 15B35; Zero-nonzero pattern; Sign pattern; Inverse;
Orthogonality to matrix subspaces, and a distance formula
Keywords: 15A60; 15A09; 47A12Birkhoff–James orthogonality; Subdifferential; Singular value decomposition; Moore–Penrose inverse; Pinching; Variance
A class of numerical algorithms for computing outer inverses
Keywords: 65F30; 65F99; 15A09; Generalized inverses; Outer inverse; Computational order of convergence; Hyperpower method;
Centralizers and their applications to generalized inverses
Keywords: 15A09; 16U80; 20M15Centralizer; Drazin inverse; Group inverse
On a matrix group constructed from an {R,s+1,k}-potent matrix
Keywords: primary; 15A09; secondary; 15A21; {R,s+1,k}-potent matrix; Group inverse; Matrix group;
Semi-convergence analysis of Uzawa methods for singular saddle point problems
Keywords: 15A09; 65F10; Singular linear systems; Saddle point problems; Uzawa method; Semi-convergence;
Componentwise enclosure for solutions of least squares problems and underdetermined systems
Keywords: 15A06; 15A09; 65F20; 65G20; 65G50Least squares problems; Underdetermined systems; Minimal 2-norm solution; Numerical enclosure; Verified error bound; Componentwise estimation
Group, Moore–Penrose, core and dual core inverse in rings with involution
Keywords: 15A09; 16U99Group inverse; Moore–Penrose inverse; Core inverse; Dual core inverse; Core-EP generalized inverse; Ring with involution; EP element; Idempotent; Inverse along an element; (b,c)(b,c)-Inverse
A block Hankel generalized confluent Vandermonde matrix
Keywords: 15A09; 15A23; 15A24; 15B99; Hankel matrix; Confluent Vandermonde matrix; Matrix polynomial;
More results on generalized Drazin inverse of block matrices in Banach algebras
Keywords: 46H05; 47A05; 15A09; Generalized Drazin inverse; Schur complement; Block matrix;
Representations for weighted Moore-Penrose inverses of partitioned adjointable operators
Keywords: 15A09; 46L08; Hilbert Câ-module; Weighted Moore-Penrose inverse; Partitioned operator;
Re-nnd generalized inverses
Keywords: 15A09; Re-nnd generalized inverse;
Moore–Penrose invertibility of differences and products of projections in rings with involution
Keywords: 15A09; 16U99; 16W10Moore–Penrose inverse; Projection; Ring with involution; ⁎-Reducing ring
Non-symbolic algorithms for the inversion of tridiagonal matrices
Keywords: 15A09; 15A15; 15A29; 39A06; 65F05; 65Y20; Computational complexity; Difference equation; Inverse matrix; Numerical algorithm; Tridiagonal matrix;
On new algorithms for inverting Hessenberg matrices
Keywords: 15A09; 15A15; 15A23; 65F05; 65Y20; Computational complexity; Hessenberg matrix; Inverse matrix; Matrix factorization;
Constraint preconditioners for solving singular saddle point problems
Keywords: 15A09; 65F10Singular linear systems; Saddle point problems; Constraint preconditioner; Convergence
The Drazin inverse of a singular, unreduced tridiagonal matrix
Keywords: 15A09; Drazin inverse; Group inverse; Tridiagonal matrix;
Schröder matrix as inverse of Delannoy matrix
Keywords: 05A05; 05A15; 05A10; 15A09; 15A36; Delannoy number; Pascal matrix; Catalan number; Schröder number; Riordan array;
A characterization of the class of partial isometries
Keywords: Primary: 47A30; 15A09; Secondary: 47B15Moore–Penrose inverse; Operator inequality; Closed range operators; Partial isometry operators
Optimal generalized ridge estimator under the generalized cross-validation criterion in linear regression
Keywords: 62J05; 62J07; 15A04; 15A09; Linear regression; Generalized ridge estimator; Linearized ridge estimator; Generalized cross-validation criterion; Hadamard product; Derivative of a vector;
On the closed representation for the inverses of Hessenberg matrices
Keywords: 11B83; 15A09; 15A15; 33C45; 47A10; 65F05General orthogonal polynomials; Hessenberg matrix; Hessenbergian; Inverse matrix; Lower semiseparable (plus diagonal) matrix; Resolvent matrix
A sharp version of Bauer–Fike’s theorem
Keywords: 15A09; 65F20Bauer–Fike’s theorem; Sign-real spectral radius; Sign-complex spectral radius; Diagonalizable; Regular matrix pair; Single-input pole placement
Solving optimization problems on ranks and inertias of some constrained nonlinear matrix functions via an algebraic linearization method
Keywords: 15A09; 15A24; 15A63; 15B10; 15B57; 65K10; 65K15
Formulas for calculating the extremum ranks and inertias of a four-term quadratic matrix-valued function and their applications
Keywords: 15A09; 15A24; 15A63; 15B57; 65K10; 90C20; 90C22Quadratic matrix-valued function; Generalized algebraic Riccati equation; Matrix inequality; Rank; Inertia; Löwner partial ordering; Optimization; Linearization method
Reverse order laws in Câ-algebras
Keywords: 15A09; Câ-algebra; Generalized inverse; MP-inverse; Reverse order law;
Primitive non-powerful symmetric loop-free signed digraphs with given base and minimum number of arcs
Keywords: 05C50; 15A09; 15A48; Primitive; Symmetric; Non-powerful; Base; Signed digraph;
Stable solutions of linear systems involving long chain of matrix multiplications
Keywords: 15A09; 15A12; 65F05; 65F35; 82B80Graded QR decomposition; Singular value decomposition; Condition number; Numerical stability; Quantum Monte Carlo
Characterizations of EP matrices and weighted-EP matrices
Keywords: 15A03; 15A09; 15A24; 15A27; EP matrix; Weighted-EP matrix; Moore-Penrose inverse; Weighted Moore-Penrose inverse; Group inverse; Commutativity; Rank formula;
Strong influence of a small fiber on shear stress in fiber-reinforced composites
Keywords: 15A15; 15A09; 15A23; High shear stress concentration; Fiber-reinforced composites; Strong effect of small inclusion; A triple of fibers; A gradient estimate;
Singularity, Wielandt’s lemma and singular values
Keywords: 15A09; 15A18; 15A06Singular values; Wielandt’s lemma; Saddle point; Block matrix