Positive semidefinite matrices are important structure matrices in many applications. For example, the covariance matrix of a random variable is positive semidefinite [2, 5]; a density matrix of a quantum system is positive semidefinite [3, 10]; a quadratic Mahalanobis distance metric can be represented by a positive semidefinite matrix as well [11]. Since $n\times n$ positive semidifinite matrices of fixed rank consist a submanifold of $\mathbb{R}^{n×n}$, it is natural to measure the difference between two such matrices by the geodesic distance on this submanifold [4, 9]. In practice, however, it is inevitable to measure the difference between two non-equidimensional positive semidefinite matrices[1]. Unfortunately, as far as we are aware, there is no existing method to deal with the situation. In this paper, we propose one such method, based on the fibre bundle structure of fixed rank positive semidefinite matrices.