Operator theory | Finite differences | Numerical differential equations | Matrix theory
Explicit formulas for eigenvalues and eigenvectors of the second derivative with different boundary conditions are provided both for the continuous and discrete cases. In the discrete case, the standard central difference approximation of the second derivative is used on a uniform grid. These formulas are used to derive the expressions for eigenfunctions of Laplacian in case of separation of variables, as well as to find eigenvalues and eigenvectors of multidimensional discrete Laplacian on a regular grid, which is presented as a Kronecker sum of discrete Laplacians in one-dimension. (Wikipedia).
With the eigenvalues for the system known, we move on the the eigenvectors that form part of the set of solutions.
From playlist A Second Course in Differential Equations
How to Find Eigenvectors Given Eigenvalues
This video explains who to find the eigenvectors that correspond to a given eigenvalue.
From playlist Eigenvalues and Eigenvectors
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Visit http://ilectureonline.com for more math and science lectures! In this video I will explain and show (in general) what is and how to find an eigenvector. Next video in this series can be seen at: https://youtu.be/SGJHiuRb4_s
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The method of determining eigenvalues as part of calculating the sets of solutions to a linear system of ordinary first-order differential equations.
From playlist A Second Course in Differential Equations
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From playlist Eigenvalues and Eigenvectors
Ex 1: Find the Eigenvalues and Corresponding Eigenvectors of a 2x2 Matrix
This video explains how to find the eigenvalues and corresponding eigenvectors of a 2x2 matrix. http://mathispower4u.com
From playlist Eigenvalues and Eigenvectors
Ex 2: Find the Eigenvalues and Corresponding Unit Eigenvectors of a 2x2 Matrix
This video explains how to find the eigenvalues and corresponding unit eigenvectors of a 2x2 matrix. http://mathispower4u.com
From playlist Eigenvalues and Eigenvectors
15. Matrices A(t) Depending on t, Derivative = dA/dt
MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018 Instructor: Gilbert Strang View the complete course: https://ocw.mit.edu/18-065S18 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP63oMNUHXqIUcrkS2PivhN3k This lecture is ab
From playlist MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018
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In this video, I leverage colorful illustrations and hands-on code demos in Python to make it intuitive and easy to understand eigenvectors and eigenvalues, concepts that may otherwise be tricky to grasp. There are eight subjects covered comprehensively in the ML Foundations series and th
From playlist Linear Algebra for Machine Learning
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Visit http://ilectureonline.com for more math and science lectures! In this video I will find eigenvector=? when given eignevalue lambda2=-1 where A is a 2x2 matrix. Next video in this series can be seen at: https://youtu.be/dN02OkJekZU
From playlist LINEAR ALGEBRA 3: EIGENVALUES AND EIGENVECTORS
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In this video, we work through some example computations of eigenvalues of 2x2 matrices. Including a case where the eigenvalues are complex numbers. We do not discuss any intuition or definition of eigenvalues or eigenvectors, we simply carry out some elementary computations. If you liked
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MIT RES.18-009 Learn Differential Equations: Up Close with Gilbert Strang and Cleve Moler, Fall 2015 View the complete course: http://ocw.mit.edu/RES-18-009F15 Instructor: Gilbert Strang An oscillation equation has 2n solutions, n cosines and n sines. Those solutions use the eigenvectors
From playlist MIT Learn Differential Equations
MIT RES.18-009 Learn Differential Equations: Up Close with Gilbert Strang and Cleve Moler, Fall 2015 View the complete course: http://ocw.mit.edu/RES-18-009F15 Instructor: Gilbert Strang The eigenvectors remain in the same direction when multiplied by the matrix. Subtracting an eigenvalue
From playlist MIT Learn Differential Equations
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