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

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

Feb 02, 2023 206 likes •523 views

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

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SLIDE 1

Bohemian Eigenvalues

Steven E. Thornton Robert M. Corless

BohemianEigenvalues.com

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SLIDE 2

Definitions

=

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SLIDE 3

× {−, , }

Example

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SLIDE 4
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SLIDE 5

⊆ ⊂ = {, }

History

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SLIDE 6

Details

Source: math.ucr.edu/home/baez/roots/

{−, }

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SLIDE 7

Eigenvalues of Random Matrices

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SLIDE 8

× {−, , } ,,

  • Details
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SLIDE 9

× {−, , }

Some Properties

  • ×

=

  • ×

=

  • ×

= ,

  • ,

× = ,, , , , ,, × = ,,, ,,

  • ,,

,,, ×

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SLIDE 10

= {, } = = ( − ) ( − ) ( − )( + ) ( − )

Duplicate Eigenvalues

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SLIDE 11

− − ! = → () () () . . .

Why Are There Repeats?

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SLIDE 12

× {−, , } [−. − ., . + .]

Details

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SLIDE 13

Details

  • ±. ± .
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SLIDE 14

Details

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SLIDE 15

× {−, , } ,,

  • Details
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SLIDE 16

Sampling

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SLIDE 17

Details

× {−, −/, , /, }

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SLIDE 18

Details

× {−, −/, , /, }

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SLIDE 19

Details

× {−, −, , , }

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SLIDE 20

Details

× {e/ | ≤ < }

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SLIDE 21

21

Details

×

  • {−, , }

[−, ]

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SLIDE 22

22

Details

×

  • {−, , }

[−.−., .+.]

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SLIDE 23

23

Details

×

  • {−, }

[− − , + ]

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SLIDE 24

24

Details

×

  • {−, , }

[− − , + ]

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SLIDE 25

25

×

  • {−, , }

[−/ − /, / + /]

Details

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SLIDE 26

26

Details

×

  • {−, , }

[− − , + ]

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SLIDE 27

Details

× − ∼ (., .)

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SLIDE 28

Details

  

  • −

−

  • −

− − −     (−, )

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SLIDE 29
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SLIDE 30
  • Future Work
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SLIDE 31

Thank You!

Source code with examples available at:

github.com/steventhornton/BHIME-Project

Coming Soon: BohemianEigenvalues.com