K-volume in Rn and the generalized Pythagorean theorem

• 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
• Institution: De La Salle University

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...