Norma inducida y bases ortonormales #SoME3

In this video, we will see the importance of characterizing the magnitudes of vectors, and introduce the concept of norm with this goal in mind, defining it through simple geometrical observations. Afterwards, we will present the process of normalization and talk about the importance of normal/unitary vectors. Then, we will show that every inner product induces a norm and, finally, we will see how orthonormal bases give us an extremely simple solution to the "problem of finding coefficients" introduced at the beginning of our previous video "Inner Product, Orthogonal Bases and Vector Projections". The code and script of the video may be consulted at Animathica's "alganim" GitHub repository: https://github.com/animathica/alganim.... This is the second video in the playlist "Inner Product Vector Spaces":    • Espacios vectoriales con producto escalar  . SCENES: 0:00 - Magnitude of vectors 2:56 - The definition of a norm 5:46 - Normal vectors and normalization 8:26 - Norms Induced by an Inner Product 10:33 - Vector projection onto a Normal Vector 11:42 - Orthonormal sets and bases 12:55 - Solution to the problem of finding coefficients with orthonormal bases 14:27 - Exercises and Questions CREDITS Script, narration and editing: Diego Alberto Barceló Nieves Animation: Juan Pablo Gamucero Arana and Diego Alberto Barceló Nieves Team coordination: Diego Alberto Barceló Nieves