Computation of Large-Dimension Jordan Normal Transform via Popular Platforms
Chunxiao Shi, Yong-Cong Chen, Xiong Xia, Ping Ao · Journal of Nonlinear Mathematical Physics · 2023
Abstract We address the practical issue that popular computation platforms like Matlab $$^{\copyright }$$ © are unable to perform the Jordan normal (canonical) form J and the associated transform matrix P on a high-dimension matrix. Given the knowledge of the eigenvalues and eigenvectors of n-square matrix A obtained on these platforms, we present an efficient algorithm of Jordan transform with detailed computation steps. The efficiency is demonstrated by comparing the simulation results of 11 examples with varying orders of n to that computed by the symbolic-based and capacity-limited routine $$[P, J] = {\textsf {jordan}}(A)$$ [ P , J ] = jordan ( A ) in Matlab $$^{\copyright }$$ © . Applications in stochastic dynamics are addressed.