K-volume in Rn and the generalized Pythagorean theorem

K-volume in Rn and the generalized Pythagorean theorem

This paper presents two generalized formulas in getting the volume of a parallelepiped generated by k vectors u1, u2, ..., uk in Rn namely: 1) IUTUI = Volume (V(U1, U2,...,Uk)2. 2) (Volume(V))2 = (Volume (P, V))2. These two formulas are proved and illustrated to facilitate the understanding of their...

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Bibliographic Details
Main Authors: Kang, Byung Woo, Gaa, Carmela M.
Format: text
Language:English
Published: Animo Repository 1998
Subjects:
Pythagorean proposition
Vector algebra
Matrices
Algebras, Linear
Online Access:https://animorepository.dlsu.edu.ph/etd_bachelors/16444
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Institution: De La Salle University
Language: English
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Summary:This paper presents two generalized formulas in getting the volume of a parallelepiped generated by k vectors u1, u2, ..., uk in Rn namely: 1) IUTUI = Volume (V(U1, U2,...,Uk)2. 2) (Volume(V))2 = (Volume (P, V))2. These two formulas are proved and illustrated to facilitate the understanding of their application. Moreover, preliminary concepts needed to tackle the main results are given.

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