Operator theory | Finite differences | Numerical differential equations | Matrix theory

Eigenvalues and eigenvectors of the second derivative

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).

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A04 Eigenvectors

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

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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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Linear Algebra: Ch 3 - Eigenvalues and Eigenvectors (5 of 35) What is an Eigenvector?

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

From playlist LINEAR ALGEBRA 3: EIGENVALUES AND EIGENVECTORS

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A03 Eigenvalues

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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Properties of Eigenvalues and Eigenvectors: Determining Ax and A(x+y) without A

This video explains how to use eigenvalue and eigenvector properties to determine Ax.

From playlist Eigenvalues and Eigenvectors

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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

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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

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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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Eigenvectors and Eigenvalues — Topic 28 of Machine Learning Foundations

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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Linear Algebra: Ch 3 - Eigenvalues and Eigenvectors (22 of 35) Given Eigenvalue, Find Eigenvector=?

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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Linear Algebra 15h: The Derivative as a Linear Transformation

https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep

From playlist Part 3 Linear Algebra: Linear Transformations

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Motivating Eigenvalues and Eigenvectors with Differential Equations

This video *derives* the eigenvalues and eigenvectors of a matrix "A" to solve the matrix system of equations dx/dt = A*x. Playlist: https://www.youtube.com/playlist?list=PLMrJAkhIeNNTYaOnVI3QpH7jgULnAmvPA Course Website: http://faculty.washington.edu/sbrunton/me564/ @eigensteve on Tw

From playlist Engineering Math: Differential Equations and Dynamical Systems

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Eigenvalues | Eigenvalues and Eigenvectors

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

From playlist Linear Algebra

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Lec 6 | MIT 18.085 Computational Science and Engineering I, Fall 2008

Lecture 06: Eigenvalues (part 2); positive definite (part 1) License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT 18.085 Computational Science & Engineering I, Fall 2008

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Scientific Computing Skills 5. Lecture 20.

UCI Chem 5 Scientific Computing Skills (Fall 2012) Lec 20. Scientific Computing Skills View the complete course: http://ocw.uci.edu/courses/chem_5_scientific_computing_skills.html Instructor: Douglas Tobias, Ph.D. License: Creative Commons BY-NC-SA Terms of Use: http://ocw.uci.edu/info.

From playlist UC Irvine Chemistry 5: Scientific Computing Skills

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Rec 3 | MIT 18.085 Computational Science and Engineering I, Fall 2008

Recitation 3 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT 18.085 Computational Science & Engineering I, Fall 2008

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Second Order Systems

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

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Eigenvalues and Eigenvectors

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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Linear Algebra: Ch 3 - Eigenvalues and Eigenvectors (6 of 35) How to Find the Eigenvector

Visit http://ilectureonline.com for more math and science lectures! In this video I will find eigenvectors=? given a 2x2 matrix and 2 eigenvalues. Next video in this series can be seen at: https://youtu.be/EaormewNDpM

From playlist LINEAR ALGEBRA 3: EIGENVALUES AND EIGENVECTORS

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Mathematics of Deep Learning: Linear Algebra III: non-linearities - Session 4

Non-linearities (Affine Maps) Non-linear Functions: Step, Sigmoid, Tanh, ReLU

From playlist Introduction to Mathematics of Deep Learning

Related pages

Discrete Laplace operator | Regular grid | Second derivative | Separation of variables | Chebyshev polynomials | Kronecker sum of discrete Laplacians