A quantitative version of the observation that the Hadamard product is a principal submatrix of the Kronecker product

DOI10.1016/S0024-3795(99)00187-1zbMath0946.15015MaRDI QIDQ1970491

George Visick

Publication date: 22 October 2000

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

zbMATH Keywords

Hadamard productcondition numbermatrix inequalitiessingular valuesKronecker productmajorizationselection matrix

Mathematics Subject Classification ID

Eigenvalues, singular values, and eigenvectors (15A18) Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Miscellaneous inequalities involving matrices (15A45) Conditioning of matrices (15A12)

Related Items (18)

Optimal \(L_2\)-norm empirical importance weights for the change of probability measure ⋮ On the Bohr inequality of operators ⋮ Norms and spread of the Fibonacci and Lucas RSFMLR circulant matrices ⋮ RETRACTED: The general (vector) solutions of such linear (coupled) matrix fractional differential equations by using Kronecker structures ⋮ Lie-Trotter formula for the Hadamard product ⋮ Further results on the vecd operator and its applications ⋮ The further generalization on the inequalities for Hadamard products of any number of invertible Hermitian matrices ⋮ Rank of a Hadamard product ⋮ Khatri-Rao products for operator matrices acting on the direct sum of Hilbert spaces ⋮ Some new connections between matrix products for partitioned and non-partitioned matrices ⋮ Extension and generalization inequalities involving the Khatri-Rao product of several ⋮ C*-algebraic Schur product theorem, P\'{o}lya-Szeg\H{o}-Rudin question and Novak's conjecture ⋮ On the norms of circulant matrices with the Fibonacci and Lucas numbers ⋮ Further inequalities involving the Khatri-Rao product ⋮ Two inequalities involving Hadamard products of positive semi-definite Hermitian matrices ⋮ Several inequalities involving Khatri-Rao products of positive semidefinite matrices ⋮ Schur complements and matrix inequalities in the Löwner ordering ⋮ The equivalent form of a matrix inequality and its application

Cites Work

• Cauchy-Schwarz inequalities associated with positive semidefinite matrices
• On majorization and Schur products
• Hölder-type norm inequalities for Schur products of matrices
• Some results on matrix monotone functions
• Concavity of certain maps on positive definite matrices and applications to Hadamard products
• Asymptotics of eigenvalues and unit-length eigenvectors of sample variance and correlation matrices
• Majorization relations for Hadamard products
• A weak majorization involving the matrices \(A\circ B\) and \(AB\)
• Several matrix Kantorovich-type inequalities
• Some eigenvalue inequalities for positive semidefinite matrix power products
• Hadamard products and multivariate statistical analysis
• Matrix Analysis
• Hadamard and conventional submultiplicativity for unitarily invariant norms on matrices
• The singular values of a Hadamard product: a basic inequality
• Partitioned and Hadamard product matrix inequalities
• Majorization and Singular Values II
• Trace and Eigenvalue Inequalities for Ordinary and Hadamard Products of Positive Semidefinite Hermitian Matrices
• Inequalities: theory of majorization and its applications
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