# under construction

## Unitary Matrices

RandomMatrix.randUnitaryFunction
randUnitary(n::Int)

Examples

Generate a 3 by 3 random Unitary matrix

randUnitary(3)

3×3 Matrix{ComplexF64}:
-0.149398+0.0572715im  -0.0935861+0.629201im  -0.257255-0.709625im
0.337035-0.342606im     -0.36366+0.599236im  -0.100838+0.517231im
-0.17097+0.845103im   -0.0767105+0.313259im   0.247081+0.3025im
source

## Orthogonal Matrices

RandomMatrix.randOrthogonalFunction
randOrthogonal(n::Int)

Examples

Generates a 3 by 3 random Orthogonal matrix

randOrthogonal(3)

3×3 Matrix{Float64}:
-0.875553  0.112448   0.469853
-0.147915  0.863441  -0.482277
0.459921  0.491757   0.739356
source

## Permutation Matrices

RandomMatrix.randPermutationFunction
randPermutation(n; fix) 
• n : dimension
• fix : a keyword argument, default is set to fix = 0. If fix = x, randPermutation(n,x) will have atleast x fixed points

Examples

Generates a random 5 by 5 permutation matrix

randPermutation(5)

5×5 SparseArrays.SparseMatrixCSC{Int8, Int64} with 5 stored entries:
⋅  ⋅  ⋅  ⋅  1
⋅  1  ⋅  ⋅  ⋅
1  ⋅  ⋅  ⋅  ⋅
⋅  ⋅  1  ⋅  ⋅
⋅  ⋅  ⋅  1  ⋅

Generates Generates a random 10 by 10 permutation matrix with atleast 7 fix points

randPermutation(10, fix = 7)

10×10 SparseArrays.SparseMatrixCSC{Int8, Int64} with 10 stored entries:
1  ⋅  ⋅  ⋅  ⋅  ⋅  ⋅  ⋅  ⋅  ⋅
⋅  1  ⋅  ⋅  ⋅  ⋅  ⋅  ⋅  ⋅  ⋅
⋅  ⋅  ⋅  ⋅  ⋅  ⋅  ⋅  ⋅  1  ⋅
⋅  ⋅  ⋅  1  ⋅  ⋅  ⋅  ⋅  ⋅  ⋅
⋮              ⋮
⋅  ⋅  ⋅  ⋅  ⋅  ⋅  1  ⋅  ⋅  ⋅
⋅  ⋅  ⋅  ⋅  ⋅  ⋅  ⋅  1  ⋅  ⋅
⋅  ⋅  1  ⋅  ⋅  ⋅  ⋅  ⋅  ⋅  ⋅
⋅  ⋅  ⋅  ⋅  ⋅  ⋅  ⋅  ⋅  ⋅  1

source