Induced Norm and Orthonormal Bases

This video shows the importance of characterizing the magnitude of vectors, introducing the concept of norm and defining it by means of simple geometrical observations. Afterward, the process of normalization and the importance of normal vectors is discussed. Then, it is shown that inner products induce norms and, finally, orthonormal bases are used to solve the problem of "finding coefficients" in an extremely simple and scalable manner. The writing and narration was done in Spanish but English subtitles are also available. It was produced in collaboration with Animathica; the video script and animation code can be found in this repository.