This paper describes a principled application of two-dimensional principal component analysis (2DPCA) to the decomposition of transformation matrices of maximum likelihood linear regression (MLLR) and its application to speaker adaptation using the bases derived from the analysis. Our previous work applied 2DPCA to speaker-dependent (SD) models to obtain the bases for state space. In this work, we apply 2DPCA to a set of MLLR transformation matrices of training speakers to obtain the bases for transformation space, since the matrices are 2-D in nature, and 2DPCA can decompose a set of matrices without vectorization. Here, we present two approaches using 2DPCA: One in eigenspace-based MLLR (ES-MLLR) framework and the other one in maximum a posteriori linear regression (MAPLR) framework. The experimental results showed that the proposed methods outperformed ES-MLLR for the adaptation data of about 10 seconds or longer.