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

with(LinearAlgebra):

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

A:=Matrix([[5,3,3,3,3],[3,5,3,3,3],[3,3,5,3,3],[3,3,3,5,3],[3,3,3,3,5]]);

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

Avec la r\303\251duite de Jordan

J:=JordanForm(A, output='J'): P:=JordanForm(A, output='Q'): jn:=DiagonalMatrix([J[1,1]^n,J[2,2]^n,J[3,3]^n,J[4,4]^n,J[5,5]^n]): An:=MatrixMatrixMultiply(P,MatrixMatrixMultiply(jn,MatrixInverse(P))); MatrixAdd(An,-MatrixPower(A,n));

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Avec les projecteurs spectraux

L := factors(MinimalPolynomial(A,x)); P:= L[2][1][1]; Q:=L[2][2][1]; gcdex(P,Q,x,'U','V'); pi1 := MatrixFunction(A,collect(P*U,x),x): pi2 := MatrixFunction(A,collect(Q*V,x),x): An := MatrixAdd(MatrixScalarMultiply(pi1,solve(Q)^n),MatrixScalarMultiply(pi2,solve(P)^n)); MatrixAdd(An,-MatrixPower(A,n));

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

Avec la division euclidienne du polyn\303\264me minimal par X^n

Eigenvalues(A);

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

assign(solve({17^n=17*a[n]+b[n],2^n=2*a[n]+b[n]},{a[n],b[n]}));

An:=MatrixAdd(MatrixScalarMultiply(A,a[n]),ScalarMatrix(b[n],5)); MatrixAdd(An,-MatrixPower(A,n));