Bohemian Eigenvalues Steven E. Thornton Robert M. Corless - PowerPoint PPT Presentation

Feb 02, 2023 •206 likes •522 views

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

Bohemian Eigenvalues Steven E. Thornton Robert M. Corless BohemianEigenvalues.com
�� Definitions �� = ��
Example � × � �� { − � , � , � } �
� �� History � �� ⊆ � �� ⊂ �� = { � , � } ��
� �� Details { − � , � } Source: math.ucr.edu/home/baez/roots/
� �� Eigenvalues of Random Matrices
� �� Details � � × � �� { − � , � , � } � � , �� , ��
� � �� Some Properties �� × � �� { − � , � , � } � � � � = � � × � � � � = �� × � � � � = �� , �� , �� × � � � � = �� , �� , �� , �� , �� , �� , �� , �� × � � � � = �� , �� , �� , �� , �� , �� , �� , �� , �� , �� , �� × � � × �
�� Duplicate Eigenvalues � �� = { � , � } � � = � �� = �� ( � − � ) � �� ( � − � ) �� ( � − � )( � + � ) � � � � ( � − � ) ��
�� Why Are There Repeats? � � �� − � �� − � �� ! � �� = � � �� → �� ( � ) �� ( � ) � �� ( � � ) � . . . ��
� �� Details � � × � �� { − � , � , � } � �� [ − � . � − � . � � , � . � + � . � � ]
� �� Details ± � . � ± � . � �
� �� Details

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