Search results with tag "Frobenius"
Lecture 17 Perron-Frobenius Theory - Stanford University
stanford.edunonnegative matrices arise in many fields, e.g., • economics • population models • graph theory • Markov chains • power control in communications • Lyapunov analysis of large scale systems Perron-Frobenius Theory 17–3
4 Singular Value Decomposition (SVD) - Princeton University
www.cs.princeton.eduquantity, the Frobenius norm of A,denoted||A|| F defined as ||A|| F = j,k a2 jk. Lemma 4.2 For any matrix A, the sum of squares of the singular values equals the Frobenius norm. That is, σ2 i (A)=||A||2 F. Proof: By the preceding discussion. AmatrixA can be described fully by how it transforms the vectors v i.Everyvector
An Introduction to Bessel Functions - Trinity University
ramanujan.math.trinity.eduBessel’s equation Frobenius’ method Γ(x) Bessel functions Bessel’s equation Given p ≥ 0, the ordinary differential equation x2y′′ +xy′ +(x2 −p2)y = 0, x > 0 (1) is known as Bessel’s equation of order p. Solutions to (1) are known as Bessel functions. Since (1) is a second order homogeneous linear equation, the
Dimensionality Reduction - Stanford University
infolab.stanford.eduThe Frobenius norm of the result is 6.971, so we divide to obtain x2 = 0.471 0.882 We are converging toward a normal vector whose second component is twice the first. That is, the limiting value of the vector that we obtain by power iteration is the principal eigenvector: x= 0.447