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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 42 "matrix algebra for the 4x4 pendula problem" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "restart;with(Linear
Algebra):with(linalg):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 13 "define matrix" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 101 "mat := Matrix([[-r,1,0,0],[-(omega^2 +Delta),-r,De
lta,0],[0,0,-r,1],[Delta,0, -(omega^2+Delta),-r]]);" }}}{EXCHG {PARA 
0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 25 "characteristic \+
polynomial" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "Determinant(m
at);factor(%);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 
0 "" {TEXT -1 28 "define transformation matrix" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 57 "C := Matrix([[1,0,1,0],[0,1,0,1],[1,0,-1,0],[0
,1,0,-1]]);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "
" {TEXT -1 34 "block diagonalization = decoupling" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 33 "Bi := multiply(inverse(C),mat,C);" }}}}
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