Eigenvalues of Random Symmetric Matrices

​
matrix element distribution
uniform
Gaussian
matrix size
40
diagonal exponent
-2
random matrix seed
difference order
0
1
2
3
4
5
Watch how the eigenvalues of random symmetric matrices approach a universal distribution as the size of the matrix increases.

Details

The eigenvalues (or their differences) are sorted, and plotted in sequence.
With diagonal exponent
p
, the constant
p
10
is added to each element on the diagonal.

External Links

Random Matrix (Wolfram MathWorld)
Wigner's Semicircle Law (Wolfram MathWorld)

Permanent Citation

Stephen Wolfram, Michael Trott
​
​"Eigenvalues of Random Symmetric Matrices"​
​http://demonstrations.wolfram.com/EigenvaluesOfRandomSymmetricMatrices/​
​Wolfram Demonstrations Project​
​Published: September 28, 2007