Bohemian Eigenvalues Joint work by: Robert M. Corless Steven E. - PowerPoint PPT Presentation

Bohemian Eigenvalues Joint work by: Robert M. Corless Steven E. Thornton Sonia Gupta Jonathan Brino-Tarasoff Venkat Balasubramanian

� �� History � �� ⊆ � �� ⊂ �� = { � , � } �� 1/29

� �� Details �� ≤ �� { − � , � } � �� 2/29 Source: math.ucr.edu/home/baez/roots/

� �� Details �� ≤ � �� − � �� 3/29 Source: math.ucr.edu/home/baez/roots/

� �� Details �� ≤ � { � , � , . . . , �� } Source: crd.lbl.gov/departments/applied-mathematics/ANAG/about/ 4/29 staff-and-postdocs/terry-ligocki/density-of-polynomial-roots/

� �� Eigenvalues of Random Matrices 5/29

� � �� Some Properties { − � , � , � } { � , � , � } { � , � , � } # � # � # � � # � # � � # � # � � 6/29

� �� Some Properties { � , � } { − � , � } { � , � } # � # � # � � # � # � � # � # � � 7/29

�� Repeats � �� = { � , � } � � = � �� = �� ( � − � ) � �� ( � − � ) �� ( � − � )( � + � ) � � � � ( � − � ) �� 8/29

�� Why Are There Repeats? � � �� − � �� − � �� ! � �� = � � �� → �� ( � ) �� ( � ) � �� ( � � ) � . . . �� 9/29

� �� Besides, We Hate Polynomials � �� 10/29

Bohemian Eigenvalues Joint work by: Robert M. Corless Steven E. - PowerPoint PPT Presentation

Bohemian Eigenvalues Joint work by: Robert M. Corless Steven E. Thornton Sonia Gupta Jonathan Brino-Tarasoff Venkat Balasubramanian

Bohemian Eigenvalues Steven E. Thornton Robert M. Corless BohemianEigenvalues.com

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Bohemian Eigenvalues Joint work by: Robert M. Corless Steven E. - PowerPoint PPT Presentation

Bohemian Eigenvalues Joint work by: Robert M. Corless Steven E. Thornton Sonia Gupta Jonathan Brino-Tarasoff Venkat Balasubramanian

Bohemian Eigenvalues Steven E. Thornton Robert M. Corless BohemianEigenvalues.com

Bohemian Rhapsody Lecture Seven The Age of Innocence TOPIC For all his aspirations and

Chapter 5 Eigenvalues and Eigenvectors Section 5.1 Eigenvectors and Eigenvalues Motivation:

Eigenvalues, Eigenvectors, Matrix Factoring, and Principal Components The eigenvalues and

Section 5.5 Complex Eigenvalues (Part II) Motivation: Complex Versus Two Real Eigenvalues

For matrix A ( p p ) with real eigenvalues, define F A , the empirical distribution function of

For matrix A ( p p ) with real eigenvalues, define F A , the empirical distribution function of

Eigenvalues, Eigenvectors, and Diagonalization Diagonalization Math 240 Calculus III Summer

Homogeneous Linear Systems Three Cases: Distinct Real Eigenvalues Repeated Eigenvalues

Matrix Calculations: Eigenvalues and Eigenvectors H. Geuvers (and A. Kissinger) Institute for

( A I ) = 0 However, there is no exact formula for polynomials of degree five

Linear Algebra Chapter 5: Eigenvalues and Eigenvectors Section 5.1. Eigenvalues and

Eigenvalues Definition 1 Given an n n matrix A , a scalar C , and a non zero vector v

Overview The previous lecture introduced eigenvalues and eigenvectors. Well review these

Eigenvalues and Eigenvectors Let A R n n be a matrix. If R and v R n , v = 0,

Computing the eigenvalues of a Joint work with Raf Vandebril and Paul Van Dooren companion

Fractional L evy processes Heikki Tikanm aki Stockholm, March 15 2010 Heikki Tikanm aki

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Embarrassingly Parallel Computations Embarrassingly Parallel Computations A computation that

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