scholarly journals Heterogeneous hypergeometric functions with two matrix arguments and the exact distribution of the largest eigenvalue of a singular beta-Wishart matrix

2021 ◽  
Vol 183 ◽  
pp. 104714
Author(s):  
Koki Shimizu ◽  
Hiroki Hashiguchi
Keyword(s):  
Hypergeometric Functions ◽  
Exact Distribution ◽  
Wishart Matrix ◽  
Largest Eigenvalue ◽  
The Largest Eigenvalue

scholarly journals The densities and distributions of the largest eigenvalue and the trace of a Beta–Wishart matrix

2019 ◽  
Vol 10 (01) ◽  
pp. 2150010
Author(s):  
Vesselin Drensky ◽  
Alan Edelman ◽  
Tierney Genoar ◽  
Raymond Kan ◽  
Plamen Koev
Keyword(s):  
Series Expansions ◽  
Wishart Matrix ◽  
Largest Eigenvalue ◽  
The Matrix ◽  
The Largest Eigenvalue

We present new expressions for the densities and distributions of the largest eigenvalue and the trace of a Beta–Wishart matrix. The series expansions for these expressions involve fewer terms than previously known results. For the trace, we also present a new algorithm that is linear in the size of the matrix and the degree of truncation, which is optimal.

scholarly journals Spectral Gap of the Largest Eigenvalue of the Normalized Graph Laplacian

2021 ◽  
Author(s):  
Jürgen Jost ◽  
Raffaella Mulas ◽  
Florentin Münch
Keyword(s):  
Lower Bound ◽  
Bipartite Graph ◽  
Spectral Gap ◽  
Complete Bipartite Graph ◽  
Graph Laplacian ◽  
New Method ◽  
Single Edge ◽  
Largest Eigenvalue ◽  
Complement Graph ◽  
The Largest Eigenvalue

AbstractWe offer a new method for proving that the maxima eigenvalue of the normalized graph Laplacian of a graph with n vertices is at least $$\frac{n+1}{n-1}$$ n + 1 n - 1 provided the graph is not complete and that equality is attained if and only if the complement graph is a single edge or a complete bipartite graph with both parts of size $$\frac{n-1}{2}$$ n - 1 2 . With the same method, we also prove a new lower bound to the largest eigenvalue in terms of the minimum vertex degree, provided this is at most $$\frac{n-1}{2}$$ n - 1 2 .

scholarly journals A note on a walk-based inequality for the index of a signed graph

2021 ◽  
Vol 9 (1) ◽  
pp. 19-21
Author(s):  
Zoran Stanić
Keyword(s):  
Adjacency Matrix ◽  
Signed Graph ◽  
Arbitrary Length ◽  
Largest Eigenvalue ◽  
The Largest Eigenvalue

Abstract We derive an inequality that includes the largest eigenvalue of the adjacency matrix and walks of an arbitrary length of a signed graph. We also consider certain particular cases.

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