Show threadkatch wreckJul 8, 2025

... that's nothing new. the point was to address a related question: suppose that the eigensystem {v_i, λ_i}, i = 1, ..., n of a full-rank, well-conditioned n-by-n square matrix A is known, and then you are given a related matrix B = A + E, where E represents some type of random noise. Can a relationship between E and c be derived, such that the eigensystem of A also satisfies f( B v_i - λ_i v_i ) <= c, for all i and some f?

#math #mathematics #linearAlgebra #eigenvalue #eigensystem #algebra

Jitse NiesenMay 16, 2025

Thanks to the Manchester NA group for organizing a seminar by David Watkins, one of the foremost experts on matrix eigenvalue algorithms. I find numerical linear algebra talks often too technical, but I could follow David's talk quite well even though I did not get everything, so thanks for that.

David spoke about the standard eigenvalue algorithm, which is normally called the QR-algorithm. He does not like that name because the QR-decomposition is not actually important in practice and he calls it the Francis algorithm (after John Francis, who developed it). It is better to think of the algorithm as an iterative process which reduces the matrix to triangular form in the limit.

#NumericalAnalysis #eigenvalue #LinearAlgebra

Pustam | पुस्तम | পুস্তম🇳🇵Jun 6, 2024

via MathMatize@X

#GaussianCurvature #EigenValue #Isometry #Invariance #IsometryInvariance #Pizza #PizzaMath #Maths #Math #MathMeme #MathsMeme #MathMemes #MathsMemes #Mathematics #Mathematicians #Mathematician

Dr. Peter RanzingerDec 21, 2023
In the world of #Eigenvalues and #Agile, it's all about identifying the unique strengths within your team. Just as Eigenvalues characterize distinctive traits of a matrix, #AgileCheese unveils the individual brilliance of each team member. Maximize your #Eigenvalue, maximize your #cheese! 🚀🧀 #AgileInsights #EigenvalueInAgility
Khurram Wadee ✅Aug 11, 2021
In the #2D #elasticity, #equilibrium of #stresses can be represented on an infinitesimal rectangular element with components of both #DirectStress and #ShearStress generally acting on all four edges. If you were to rotate the rectangle, the stresses change in a precisely orchestrated fashion. In the orientation where the shear stress components vanish, we get what are called #PrincipalStresses and they and their directions can be ascertained precisely through #eigenvalue analysis... 1/2
xameerMay 31, 2021
#Maxwell's equations+ curl of Ohm's law : derive a linear #eigenvalue equation for (B), assuming B is independent from velocity field-> critical B Reynolds number, above which flow strength is sufficient to amplify imposed B, and below which B dissipates.
xameerMay 29, 2021
Watch "10.1.1 Power Method to compute second #eigenvalue, implementation Part 2" on YouTube - https://youtu.be/YmZc2oq02kA
Can't help
10.1.1 Power Method to compute second eigenvalue, implementation Part 2

YouTube
xameerMay 2, 2021
- differential equation containing the Laplace operator is then transformed into a variational formulation, and a system of equations is constructed (linear or #eigenvalue problems). The resulting matrices are usually very sparse and can be solved with iterative methods. #fem
xameerApr 6, 2021
as long as a ~ a characteristic n, c_2is not identically 0 , divergent solution eventually dominates for large enough r
Hence semi-analytical/numerical ways : a continued fraction expansion,casting recurrence as a matrix #eigenvalue problem, a backwards recurrence algorithm.
xameerDec 27, 2020
Watch "Self-adjoint operators have eigenvalues" on YouTube - https://youtu.be/SvF4ezFKWqo
An operator doesn't need an inner product to have an #eigenvalue
Self-adjoint operators have eigenvalues

This is a series of videos that I have incorporated into my VoiceThread(R) lectures of a course Honors Linear Algebra II. The course is taught entirely onlin...