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Equilateral dimension of the Riemannian manifold of $2 \times 2$ positive definite matrices
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We mainly prove that the equilateral dimensions of the Riemannian manifolds consisting of $2 \times 2$ invertible density matrices and positive definite matrices with determinant $1$ are respectively $4$. We also give the minimum of equilateral dimension of the Cartan-Hadamard manifold consisting of positive definite (Hermitian) matrices.
Abstract
We mainly prove that the equilateral dimensions of the Riemannian manifolds consisting of $2 \times 2$ invertible density matrices and positive definite matrices with determinant $1$ are respectively $4$. We also give the minimum of equilateral dimension of the Cartan-Hadamard manifold consisting of positive definite (Hermitian) matrices.
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