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Constructing Invariant Subspaces As Kernels Of Commuting Matrices, Carl C. Cowen, William Johnston, Rebecca G. Wahl
Constructing Invariant Subspaces As Kernels Of Commuting Matrices, Carl C. Cowen, William Johnston, Rebecca G. Wahl
Scholarship and Professional Work - LAS
Given an n n matrix A over C and an invariant subspace N, a straightforward formula constructs an n n matrix N that commutes with A and has N = kerN. For Q a matrix putting A into Jordan canonical form, J = Q􀀀1AQ, we get N = Q􀀀1M where M= ker(M) is an invariant subspace for J with M commuting with J. In the formula J = PZT􀀀1Pt, the matrices Z and T are m m and P is an n m row selection matrix. If N is a marked subspace, m = n and Z is an n …