23.9.2011 Jaroslav Kautsky (Flinders University, Australia) Generalized Toeplitz-Pascal matrices and bi-diagonal LU factorization Abstract: ========= A class of matrices which are the Hadamard product of a fixed lower triangular generating matrix P and any Toeplitz matrix is studied. Conditions on P which lead to the class being closed under matrix multiplication are derived and such generating matrices are fully characterized. This generalizes the special cases when either P itself is Toeplitz or P is the Pascal triangle but the Toeplitz matrix is generated by the vector of powers. Explicit formulae for inverses are derived and commutativity of products within each class proven. Examples using generalized Pascal triangles are shown. The known factorization of the Pascal triangle/power Toeplitz matrix into a product of bi-diagonal matrices is generalized for any matrix with certain non-vanishing minors. Motivation for the study of these properties came from the bad condition of the Pascal triangle matrix which causes difficulties in the evaluation of blur invariants of higher degrees. That problem is, however, unresolved.