Orthonormal Vectors Properties

This lecture covers the properties of orthonormal vectors in an Euclidean space, focusing on proving key equations involving scalar products and vector norms. The instructor demonstrates how to show that the norm of the difference between two orthonormal vectors is the square root of 2, and how to derive the difference of the norms of the sum and difference of two vectors. Additionally, the lecture explains how to prove an equation involving the norms of the sum and difference of any two vectors in the space. Through detailed calculations and explanations, the instructor provides a comprehensive understanding of the properties of orthonormal vectors.