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ThmDex – An index of mathematical definitions, results, and conjectures.
Characteristic polynomial for a lower triangular complex matrix
Formulation 0
Let ACN×N be a D6159: Complex square matrix such that
(i) A is a D5949: Lower triangular complex matrix
(ii) A=[A1,100A2,1A2,20AN,1AN,2AN,N]
Let zC be a D1207: Complex number.
Then Det(zINA)=Nn=1(zAn,n)
Proofs
Proof 0
Let ACN×N be a D6159: Complex square matrix such that
(i) A is a D5949: Lower triangular complex matrix
(ii) A=[A1,100A2,1A2,20AN,1AN,2AN,N]
Let zC be a D1207: Complex number.
This result is a particular case of R5560: Characteristic polynomial for a triangular complex matrix.