So I am reading a paper (https://www.researchgate.net/publication/263699451_From_Manifold_to_Manifold_Geometry-Aware_Dimensionality_Reduction_for_SPD_Matrices) during which the author states that "SPD matrices can be thought of as an extension of positive numbers and form the interior of the positive semidefinite cone".
I understand how one can show that the SPD space is conical (at least simply and in 2D) but I have no idea how this can be related to positive numbers (Other than the fact that the eigenvalues of every matrix must be positive)
Could anyone elaborate further as to what the author means?