Visualizing Cauchy’s Interlacing Property for Line Distance Matrices

author: Gašper Jaklič, IMFM

Description

In the paper it is proven that line distance matrices of size n have one positive and n ! 1 negative eigenvalues. Visual representation of Cauchy's interlacing property for line distance matrices is considered.

Categories

Top: Mathematics

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*Slides*
0:01	Visualizing Cauchy’s Interlacing Property for Line Distance Matrices
0:59	Motivation
2:15	Line distance matrices
3:09	Human -globin gene
5:35	Properties of line distance matrices
6:42	Cauchy’s interlacing theorem
8:08	The number of negative eigenvalues
9:33	Example
10:14	Example
11:23	Cauchy’s interlacing property
12:51	Eigenvalues of line distance matrices
14:49	Key observations
17:21	Key observations
18:31	Key observations
18:35	Key observations
18:58	Key observations
20:20	Example
21:38	Visualization
22:51	Visualization: -globin
23:32	Further work
24:25	Visualization: -globin
24:43	Further work
26:30	Visualization: -globin
27:05	Cauchy’s interlacing property
27:34	Visualization: -globin
27:41	Further work
27:58	Visualization: -globin

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