InvertibleMatrices{๐ฝ,T} <: AbstractDecoratorManifold{๐ฝ}The AbstractManifold consisting of the real- or complex-valued invertible matrices, that is the set
manifold_dimension(M::InvertibleMatrices{n,๐ฝ})Return the dimension of the InvertibleMatrices matrix M over the number system ๐ฝ, which is the same dimension as its embedding, the Euclidean(n, n; field=๐ฝ).
manifold_dimension(M::CenteredMatrices)Return the manifold dimension of the CenteredMatrices m-by-n matrix M over the number system ๐ฝ, i.e.
manifold_dimension(M::CholeskySpace)Return the manifold dimension for the CholeskySpace M, i.e.
manifold_dimension(M::Circle)Return the dimension of the Circle M, i.e. .
manifold_dimension(M::DeterminantOneMatrices{n,๐ฝ})Return the dimension of the DeterminantOneMatrices matrix M over the number system ๐ฝ, which is one dimension less than its embedding, the Euclidean(n, n; field=๐ฝ).
manifold_dimension(M::Elliptope)returns the dimension of Elliptope M , i.e.
manifold_dimension(M::EssentialManifold{is_signed, โ})Return the manifold dimension of the EssentialManifold, which is 5[TD17].
manifold_dimension(M::Euclidean)Return the manifold dimension of the Euclidean M, i.e. the product of all array dimensions and the real_dimension of the underlying number system.
manifold_dimension(M::FixedRankMatrices)Return the manifold dimension for the ๐ฝ-valued FixedRankMatrices M of dimension mxn of rank k, namely
manifold_dimension(M::Flag)Return dimension of flag manifold .
manifold_dimension(M::GeneralizedGrassmann)Return the dimension of the GeneralizedGrassmann(n,k,๐ฝ) manifold M, i.e.
manifold_dimension(M::GeneralizedStiefel)Return the dimension of the GeneralizedStiefel manifold M=.
manifold_dimension(M::Rotations)
manifold_dimension(M::OrthogonalMatrices)Return the dimension of the manifold orthogonal matrices and of the manifold of rotations
manifold_dimension(M::SpecialUnitaryMatrices)Return the dimension of the manifold of special unitary matrices.
manifold_dimension(M::UnitaryMatrices{n,โ}) where {n}Return the dimension of the manifold unitary matrices.
manifold_dimension(M::UnitaryMatrices{<:Any,โ})Return the dimension of the manifold unitary matrices.
manifold_dimension(N::GraphManifold{G,๐ฝ,M,EdgeManifold})returns the manifold dimension of the GraphManifold N on the edges of a graph , i.e.
manifold_dimension(N::GraphManifold{G,๐ฝ,M,VertexManifold})returns the manifold dimension of the GraphManifold N on the vertices of a graph , i.e.
manifold_dimension(M::Grassmann)Return the dimension of the Grassmann(n,k,๐ฝ) manifold M, i.e.
manifold_dimension(M::HeisenbergMatrices)Return the dimension of HeisenbergMatrices(n), which is equal to .
manifold_dimension(M::Hyperbolic)Return the dimension of the hyperbolic space manifold , i.e. .
manifold_dimension(M::Hyperrectangle)Return the manifold dimension of the Hyperrectangle M, i.e. the product of all array dimensions.
manifold_dimension(M::MultinomialDoubleStochastic)returns the dimension of the MultinomialDoubleStochastic manifold namely
manifold_dimension(M::MultinomialSymmetric)returns the dimension of the MultinomialSymmetric manifold namely
manifold_dimension(M::PositiveNumbers)Return the dimension of the PositiveNumbers M, i.e. of the 1-dimensional hyperbolic space,
manifold_dimension(M::ProbabilitySimplex)Returns the manifold dimension of the probability simplex in , i.e.
manifold_dimension(M::AbstractProjectiveSpace{๐ฝ}) where {๐ฝ}Return the real dimension of the AbstractProjectiveSpace M, respectively i.e. the real dimension of the embedding minus the real dimension of the field ๐ฝ.
manifold_dimension(M::KendallsPreShapeSpace)Return the dimension of the KendallsPreShapeSpace manifold M.
manifold_dimension(M::KendallsShapeSpace)Return the dimension of the KendallsShapeSpace manifold M.
manifold_dimension(M::SkewHermitianMatrices)Return the dimension of the SkewHermitianMatrices matrix M over the number system ๐ฝ, i.e.
manifold_dimension(M::Spectrahedron)returns the dimension of Spectrahedron M, i.e.
manifold_dimension(M::AbstractSphere)Return the dimension of the AbstractSphere M, respectively i.e. the dimension of the embedding -1.
manifold_dimension(M::SphereSymmetricMatrices{<:Any,๐ฝ})Return the manifold dimension of the SphereSymmetricMatrices n-by-n symmetric matrix M of unit Frobenius norm over the number system ๐ฝ, i.e.
manifold_dimension(M::Stiefel)Return the dimension of the Stiefel manifold M=.
manifold_dimension(M::SymmetricMatrices{n,๐ฝ})Return the dimension of the SymmetricMatrices matrix M over the number system ๐ฝ, i.e.
manifold_dimension(M::SymmetricPositiveDefinite)returns the dimension of SymmetricPositiveDefinite M , i.e.
manifold_dimension(M::SymmetricPositiveSemidefiniteFixedRank)Return the dimension of the SymmetricPositiveSemidefiniteFixedRank matrix M over the number system ๐ฝ, i.e.
rand(::SymplecticMatrices; vector_at=nothing, ฯ::Real=1.0)Generate a random point on or a random tangent vector if vector_at is set to a point .
manifold_dimension(::SymplecticMatrices)Returns the dimension of the symplectic manifold embedded in , i.e.
manifold_dimension(::SymplecticGrassmann)Return the dimension of the SymplecticGrassmann(2n,2k), which is
manifold_dimension(::SymplecticStiefel)Returns the dimension of the symplectic Stiefel manifold embedded in , i.e. [BZ21]
manifold_dimension(M::EmbeddedTorus)Return the dimension of the EmbeddedTorus M that is 2.
manifold_dimension(::Tucker)The dimension of the manifold of tensors of multilinear rank , i.e.