Explain how, for each € ≥ 0, one can associate a clique complex Ke to a symmetric n x n matrix of distances between n items. For € = 2.5 and for the following 6 x 6 matrix of distances 0 1 2 3 3 3 10 1 3 3 3 210 1 3 3 3 3 1 0 1 2 3 3 10 1 3 3 3 2 1 0 determine the simplicial complex Ke; then sketch the geometric realization |Ke and calculate the Euler characteristic x(K₂).

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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3. Explain how, for each e > 0, one can associate a clique complex Ke to a symmetric ñ × n
matrix of distances between n items.
For € = 2.5 and for the following 6 x 6 matrix of
distances
0
1 2 3 3 3
101
3 3 3
210
1
3 3
3 3 1
0 1 2
3 3 3
1
0 1
3 3 3 2 1 0
determine the simplicial complex Ke; then sketch the geometric realization |Ke and calculate
the Euler characteristic x(K).
Transcribed Image Text:3. Explain how, for each e > 0, one can associate a clique complex Ke to a symmetric ñ × n matrix of distances between n items. For € = 2.5 and for the following 6 x 6 matrix of distances 0 1 2 3 3 3 101 3 3 3 210 1 3 3 3 3 1 0 1 2 3 3 3 1 0 1 3 3 3 2 1 0 determine the simplicial complex Ke; then sketch the geometric realization |Ke and calculate the Euler characteristic x(K).
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