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Visualizing Cauchy’s Interlacing Property for Line Distance Matrices
Published on Feb 25, 20074836 Views
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 c
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Chapter list
Visualizing Cauchy’s Interlacing Property for Line Distance Matrices00:01
Motivation00:59
Line distance matrices02:15
Human -globin gene03:09
Properties of line distance matrices05:35
Cauchy’s interlacing theorem06:42
The number of negative eigenvalues08:08
Example09:33
Example10:14
Cauchy’s interlacing property11:23
Eigenvalues of line distance matrices12:51
Key observations14:49
Key observations17:21
Key observations18:31
Key observations18:35
Key observations18:58
Example20:20
Visualization21:38
Visualization: -globin22:51
Further work23:32
Visualization: -globin24:25
Further work24:43
Visualization: -globin26:30
Cauchy’s interlacing property27:05
Visualization: -globin27:34
Further work27:41
Visualization: -globin27:58