The generalized sine theorem and inequalities for simplices

DOI10.1016/S0024-3795(97)10096-9zbMath0937.51013MaRDI QIDQ1307292

Yao Zhang, Gang Song Leng

Publication date: 28 October 1999

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

zbMATH Keywords

determinantvertex anglesdihedral angleregular simplex\(n\)-simplex\(n\)-parallelotopesine theorem

Mathematics Subject Classification ID

Inequalities and extremum problems in real or complex geometry (51M16)

Related Items (9)

Volumes of \(s\)-Orlicz convex simplices and geometric inequalities in higher dimensional spaces ⋮ The open mouth theorem in higher dimensions ⋮ Pre-kites: simplices having a regular facet ⋮ Inequalities for vertex distances of two simplices ⋮ Vertex angles of a simplex in hyperbolic space \(H^n\) ⋮ On \(d\)-dimensional \(d\)-semimetrics and simplex-type inequalities for high-dimensional sine functions ⋮ On the Schlafli differential formula based on edge lengths of tetrahedron in \(H^{3}\) and \(S^{3}\) ⋮ Refinements of the Hadamard and Cauchy-Schwarz inequalities with two inequalities of the principal angles ⋮ Inequalities for two simplices

Cites Work

• Determinantal identities: Gauss, Schur, Cauchy, Sylvester, Kronecker, Jacobi, Binet, Laplace, Muir, and Cayley
• The law of sines for tetrahedra and \(n\)-simplices
• The sine theorem and inequalities for volumes of simplices and determinants
• Some inequalities on the inradii of a simplex and of its faces
• A matrix inequality with weights and its applications
• Matrix Analysis
• The sine theorem for simplexes in $E_n$
• Determinantensätze und Simplexeigenschaften (Verallgemeinerung trigonometrischer Lehrsätze auf n‐dimensionale Simplexe)
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