Cholesky-Zerlegung :restart : Digits:=6: with(LinearAlgebra);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:=10 :L:=Matrix(1..n,1..n,0): A:=Matrix(1..n,1..n,0):#A:=Matrix([[9 , 45 , -9 , -18 ], [ 45 , 234 , -48 , -93 ],[ -9 , -48 , 19 , 19 ], [ -18 , -93 , 19 , 46 ]]);for i from 1 by 1 while i <= n do for k from 1 by 1 while k <= n do if i = k then A[i,k]:= 1; else A[i,k]:= (i+k-1)*0.05 end if; end do: end do: A;NiMtSSdSVEFCTEVHNiI2JSIoKVtCNi1JJ01BVFJJWEdGJTYjNyw3LCIiIiQiIzUhIiMkIiM6RjAkIiM/RjAkIiNERjAkIiNJRjAkIiNORjAkIiNTRjAkIiNYRjAkIiNdRjA3LEYuRi1GM0Y1RjdGOUY7Rj1GPyQiI2JGMDcsRjFGM0YtRjdGOUY7Rj1GP0ZCJCIjZ0YwNyxGM0Y1RjdGLUY7Rj1GP0ZCRkUkIiNsRjA3LEY1RjdGOUY7Ri1GP0ZCRkVGSCQiI3FGMDcsRjdGOUY7Rj1GP0YtRkVGSEZLJCIjdkYwNyxGOUY7Rj1GP0ZCRkVGLUZLRk4kIiMhKUYwNyxGO0Y9Rj9GQkZFRkhGS0YtRlEkIiMmKUYwNyxGPUY/RkJGRUZIRktGTkZRRi0kIiMhKkYwNyxGP0ZCRkVGSEZLRk5GUUZURldGLUknTWF0cml4RzYkSSpwcm90ZWN0ZWRHRmZuSShfc3lzbGliR0Ylpos_def:=IsDefinite(A);NiM+SShwb3NfZGVmRzYiSSV0cnVlR0kqcHJvdGVjdGVkR0YnL[1,1]:=sqrt(A[1,1]): for j from 2 by 1 while j <= n do L[j,1]:= A[j,1] / L[1,1] ; end do : for i from 2 by 1 while i <= n-1 do L[i,i]:= sqrt( A[i,i] - add( L[i,k]*L[i,k], k=1..i-1) ); for j from i+1 by 1 while j <= n do L[j,i]:= 1/L[i,i] * (A[j,i] - add( L[j,k]*L[i,k], k=1..i-1) ); end do : end do : L[n,n]:=sqrt( A[n,n] - add( L[n,k]*L[n,k], k=1..n-1) ):eval(L); LinearAlgebra:-Transpose(Matrix(L));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