Diagonalizability of Matrices
Una introducción a los eigenvalores y eigenfunciones para un Sistema Lineal Invariente en el Tiempo.
An introduction to eigenvalues and eigenfunctions for Linear Time Invariant systems.
This module provides a brief overview and review of the importance of eigenvectors and eigenvalues in analyzing and understanding LTI systems.
This module defines eigenvalues and eigenvectors and explains a method of finding them given a matrix. These ideas are presented, along with many examples, in hopes of leading up to an understanding of the Fourier Series.
This module defines eigenvalues and eigenvectors and explains a method of finding them given a matrix. These ideas are presented, along with many examples, in hopes of leading up to an understanding of the Fourier Series.
Este modulo nos da un pequeño repaso de la importancia de los eigenvectores y eigenvalores en el análisis y entedimiento de los sistemas LTI.
This course covers the mathematical techniques necessary for understanding of materials science and engineering topics such as energetics, materials structure and symmetry, materials response to applied fields, mechanics and physics of solids and soft materials. The class uses examples from the materials science and engineering core courses (3.012 and 3.014) to introduce mathematical concepts and materials-related problem solving skills. Topics include linear algebra and orthonormal basis, eigenvalues and eigenvectors, quadratic forms, tensor operations, symmetry operations, calculus of several variables, introduction to complex analysis, ordinary and partial differential equations, theory of distributions, and fourier analysis. Users may find additional or updated materials at Professor Carter's 3.016 course Web site.
This module introduces how to compute the matrix exponential using eigenvalues and eigenvectors.
The notes contained herein outline the delta-x of the Riemann sum equation transformation into a function used to find the area spectrum of a data set. The transformation uses an eigenfunction by expanding the data set arrays into eigenvecotrs.
This course covers the derivation of symmetry theory; lattices, point groups, space groups, and their properties; use of symmetry in tensor representation of crystal properties, including anisotropy and representation surfaces; and applications to piezoelectricity and elasticity.
