Show that for the vector L₁ norm ||u||₁ = }}=₁|u;], where u = (u₁, U2, ..., un), the subordinate matrix L₁ norm defined by || A||₁ = max ||Au||₁, is the maximum absolute column sum, that is n ||A||₁ = max Σlail. 1sjsn i=1

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Show that for the vector L₁ norm ||u||₁ = Σ}=1|u;], where u =
(U₁, U₂, ..., un), the subordinate matrix L₁ norm defined by ||A||₁ = max || Au||₁, is the
maximum absolute column sum, that is
n
||A||₁ = max Σlaijl.
1sjsn
i=1
Transcribed Image Text:Show that for the vector L₁ norm ||u||₁ = Σ}=1|u;], where u = (U₁, U₂, ..., un), the subordinate matrix L₁ norm defined by ||A||₁ = max || Au||₁, is the maximum absolute column sum, that is n ||A||₁ = max Σlaijl. 1sjsn i=1
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