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

Sep 05, 2022 •347 likes •677 views

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

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

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