Matrix joint block diagonalization problem is a particular block term 
decomposition of third order tensors, which has many 
important applications in blind source separation and independent 
component analysis. In this talk, I will talk about two classes 
of algebraic methods for JBD problem: one is based on matrix 
polynomial, the other is based on matrix commutation. 
Existence and uniqueness conditions for JBD problem are discussed. 
Numerical methods are developed and validated by simulating examples. 
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