On an inequality related to the volume of a parallelepiped

The problem of establishing an upper bound for the volume of a parallelepiped is considered by utilizing an original approach involving a skew-symmetric matrix of order four (along with its Moore–Penrose inverse). It is shown that the commonly known inequality characterizing the bound can be virtual...

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Bibliographic Details
Published inExamples and counterexamples Vol. 6; p. 100155
Main Authors Baksalary, Oskar Maria, Trenkler, Götz
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.12.2024
Elsevier
Subjects
Antisymmetric matrix
Cauchy–Schwarz inequality
Characteristic polynomial
Cross-product matrix
Moore–Penrose inverse
Quaternion
Robotics
Rotation matrix
Scalar product
Rotation matrix
Cauchy–Schwarz inequality
Antisymmetric matrix
Moore–Penrose inverse
Scalar product
Quaternion
15A10
Characteristic polynomial
Cross-product matrix
2020
15B57
Robotics
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Summary:The problem of establishing an upper bound for the volume of a parallelepiped is considered by utilizing an original approach involving a skew-symmetric matrix of order four (along with its Moore–Penrose inverse). It is shown that the commonly known inequality characterizing the bound can be virtually sharpened. Similarly, a sharpening is established with respect to the Cauchy–Schwarz inequality. General properties of the Moore–Penrose inverse of a skew-symmetric matrix are discussed as well.
ISSN:2666-657X
2666-657X
DOI:10.1016/j.exco.2024.100155