Matrices of determinant one

Manifolds.DeterminantOneMatrices โ€” Type
DeterminantOneMatrices{๐”ฝ,T} <: AbstractDecoratorManifold{๐”ฝ}

The AbstractManifold consisting of the real- or complex-valued (invertible) matrices od determinant one, that is the set

\[\bigl\{p โˆˆ ๐”ฝ^{nร—n}\ \big|\ \det(p) = 1 \bigr\},\]

where the field $๐”ฝ โˆˆ \{ โ„, โ„‚\}$.

Note that this is a subset of InvertibleMatrices, and a superset of any of the GeneralUnitaryMatrices

The tangent space at any point p is the set of matrices with trace 0.

Constructor

DeterminantOneMatrices(n::Int, field::AbstractNumbers=โ„)

Generate the manifold of $nร—n$ matrices of determinant one.

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Base.rand โ€” Method
Random.rand(M::DeterminantOneMatrices; vector_at=nothing, kwargs...)

If vector_at is nothing, return a random point on the DeterminantOneMatrices manifold M by using rand in the embedding.

If vector_at is not nothing, return a random tangent vector from the tangent space of the point vector_at on the DeterminantOneMatrices by using by using rand in the embedding.

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ManifoldsBase.check_point โ€” Method
check_point(M::DeterminantOneMatrices{n,๐”ฝ}, p; kwargs...)

Check whether p is a valid manifold point on the DeterminantOneMatrices M, i.e. whether p has a determinant of $1$.

The check is perfomed with isapprox and all keyword arguments are passed to this

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