Norm inequalities related to clarkson inequalities

Citation data:

Electronic Journal of Linear Algebra, ISSN: 1081-3810, Vol: 34, Issue: 1, Page: 163-169

Publication Year:
2018
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Repository URL:
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DOI:
10.13001/1081-3810,1537-9582.3642; 10.13001/1081-3810,1537-9582.3528; 10.13001/1081-3810, 1537-9582.3200; 10.13001/1081-3810, 1537-9582.3649; 10.13001/1081-3810,1537-9582.3449; 10.13001/1081-3810,1537-9582.3530; 10.13001/1081-3810, 1537-9582.3741; 10.13001/1081-3810,1537-9582.3595; 10.13001/1081-3810, 1537-9582.3609; 10.13001/1081-3810, 1537-9582.3121; 10.13001/1081-3810, 1537-9582.2982; 10.13001/1081-3810, 1537-9582.3588; 10.13001/1081-3810,1537-9582.3416; 10.13001/1081-3810,1537-9582.3510; 10.13001/1081-3810, 1537-9582.3635; 10.13001/1081-3810, 1537-9582.3636; 10.13001/1081-3810, 1537-9582.3467; 10.13001/1081-3810, 1537-9582.3613; 10.13001/1081-3810, 1537-9582.3449; 10.13001/1081-3810, 1537-9582.3647; 10.13001/1081-3810, 1537-9582.3671; 10.13001/1081-3810, 1537-9582.3416; 10.13001/1081-3810, 1537-9582.3732; 10.13001/1081-3810, 1537-9582.3595; 10.13001/1081-3810, 1537-9582.3542; 10.13001/1081-3810, 1537-9582.3793; 10.13001/1081-3810, 1537-9582.3654; 10.13001/1081-3810, 1537-9582.3528; 10.13001/1081-3810, 1537-9582.3493; 10.13001/1081-3810, 1537-9582.3774; 10.13001/1081-3810, 1537-9582.3555; 10.13001/1081-3810, 1537-9582.3733; 10.13001/1081-3810, 1537-9582.3748; 10.13001/1081-3810, 1537-9582.3688; 10.13001/1081-3810, 1537-9582.3642; 10.13001/1081-3810, 1537-9582.3727; 10.13001/1081-3810, 1537-9582.3743; 10.13001/1081-3810, 1537-9582.3510; 10.13001/1081-3810, 1537-9582.3651; 10.13001/1081-3810, 1537-9582.3665; 10.13001/1081-3810, 1537-9582.3616; 10.13001/1081-3810, 1537-9582.3600; 10.13001/1081-3810, 1537-9582.3530; 10.13001/1081-3810, 1537-9582.3746
Author(s):
Aalipour, Ghodratollah; Abiad, Aida; Berikkyzy, Zhanar; Hogben, Leslie; Kenter, Franklin H.J.; Lin, Jephian C.-H.; Tait, Michael
Tags:
Mathematics; Block trace operator; Partial trace operator; Block matrix; Algebra; Applied Statistics; distance matrix; characteristic polynomial; unimodal; log-concave; Discrete Mathematics and Combinatorics; Other Applied Mathematics; Numerical range; maximal numerical range; normaloid matrices; Analysis; Octagonal chains; Spectral radius; Extremal graphs; Diffeological space; diffeological vector space; diffeologically smooth bilinear form; Geometry and Topology; Wishart matrix; multivariate normal distribution; spectral distribution; spectral moments; covariance matrix; Other Statistics and Probability; Probability; Distance matrix; Distance eigenvalue; Distance spectral radius; Distance signless Laplacian matrix; Ger$\check{s}$gorin disc; Physical Sciences and Mathematics; copositive matrix; extreme ray; zero support set; the largest eigenvalue; Hamiltonian property; rank-function; generalized inverse; outer inverse; Drazin Inverse; Matrix over Commutative ring; Positivity and semipositivity of linear maps; proper cones; positive definite matrices; positive stable matrices; semidefinite linear complementarity problems; Lyapunov and Stein transformations; semipositive cone; Other Mathematics; Positive definite matrices; Matrix inequalities; perturbation upper bounds; subunitary polar factor; unitarily invariant norm; $Q$-norm; Quadratic matrix equation; Verified numerical computation; Dominant solvent; Minimal solvent; Numerical Analysis and Computation; tropical semiring; symmetric matrix; rank; Quadratic subspace; Testing hypotheses; Structure of covariance matrices; Positive and negative part of estimator; Block compound symmetric covariance structure; Double multivariate data; Multivariate Analysis; Statistical Methodology; Statistical Models; Perron-Frobenius theory; Correlation matrix; Positive eigenvector; Hafnian; Permanent; Pfaffian; Determinant; Grassmann algebra; Irregular graph; eigenvector; principal ratio; sign pattern; zero-nonzero pattern; inertia; digraph; R\'enyi entropy; R\'enyi relative entropy; partition function; Helmholtz free energy; $\alpha$-variance; Semipositive matrix; minimally semipositive matrix; principal pivot transform; Moore-Penrose inverse; left inverse; interval of matrices; Matrix equation; Symmetric positive definite; Fixed-point iteration; Condition number; Mixed and componentwise.; Algebraic graph theory; eigenspaces; quantum walks; Distance spectrum; Complement; Cospectral.; Markov chains; Zero forcing; Parameter identification.; Control Theory; Distinct eigenvalues; Perturbation; Geometric multiplicity; Algebraic multiplicity; Range-compatibility; fields with two elements; evaluation map; algebraic reflexivity; Quantum state; reduced state; partial trace; quantum channel; eigenvalue.; Determinantal representation; elliptic curves; Weierstrass $\wp$-functions; Riemann theta functions.; Algebraic Geometry; Clarkson inequalities; Hanner's inequality; Schatten p-norm; L_p function; Singular value; Best unbiased estimator; testing structured mean vector; blocked compound symmetric covariance structure; doubly multivariate data; coordinate free approach; unstructured mean vector; Constant sum matrix; eigenvalue; quasi-inverse matrix; numerical range; finite field; Hermitian variety over a finite field; Algebraic-difference equation; behavior; exact modeling; auto-regressive representation; discrete time system; higher order system; descriptor system; Dynamic Systems; Hilbert $C^*$-module; Operator equation; Solution; Orthogonally complemented
article description
Let A and B be n × n matrices. It is shown that if p = 2, 4 ≤ p < ∞, or 2 < p < 4, and both A + B, A − B are positive semidefinite, then) ( ∣ ∣ ‖A + B‖pp‖A‖pp − 2p − 2) − ‖B‖and if p = 2, 4 ≤ p < ∞, or 2 < p < 4, and both A, B are positive semidefinite, then) ∣ ‖A + B‖pp (‖A‖pp + (2− 2∣p) ∣‖A + B‖− ‖A − B‖These inequalities are reversed if p = 2, 1 ≤ p ≤3< p < 2, and both A + B, A − B are positive semidefinite, and if 3 p = 2, 1 ≤ p ≤3< p < 2, and both A, B are positive semidefinite, respectively. Commutative (or Lp) versions of these 3 inequalities are also considered.