ORTHOGONALITY IN N-INNER PRODUCT SPACE

• Main Author: Adam
• Format: Final Project
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/47748
• Institution: Institut Teknologi Bandung

The orthogonality concept in n-inner product space was published by various mathematicians. Starting from the orthogonality concept by Khan and Siddiqui then Cho and Kim to Godini, the orthogonality concept which is called G-orthogonality was developed more precisely by Gunawan et al. But this concept does not include the n-dimensional case. Using the concept for the n-dimensional case will make any two vectors are orthogonal. Furthermore, a new orthogonality concept is needed for n-dimensional n-inner product space. Using the fact that the inner product can be induced through the n-inner product, the author constructs a new concept of orthogonality based on this inner product. In general, in standard n-inner product space, the orthogonality of two vectors based on the initial inner product is not preserved by the new inner product obtained from n-inner product. Then the author investigates when two orthogonal vectors based on the initial inner product remain orthogonal also based the new inner product obtained from n-inner product.