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J. M.'s missing motivation
J. M.'s missing motivation
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RandomVariate[NormalDistribution[], {r, r}] does not give you normalized eigenvectors. To obtain an orthonormal basis, you can first generate a random matrix, and then apply OrthogonalizeOrthogonalize to it. Following is the correct code.

r=4;(*matrix dimension*) dom={1,10};(*domain of random numbers*) eig=DiagonalMatrix[-RandomInteger[dom,r]] (*eigenvalues in diagonal matrix*) v=Orthogonalize@RandomVariate[NormalDistribution[], {r, r}](*orthonormal eigenvectors*) A=Transpose[v].eig.v Eigenvalues[A]

RandomVariate[NormalDistribution[], {r, r}] does not give you normalized eigenvectors. To obtain an orthonormal basis, you can first generate a random matrix, and then apply Orthogonalize to it. Following is the correct code.

r=4;(*matrix dimension*) dom={1,10};(*domain of random numbers*) eig=DiagonalMatrix[-RandomInteger[dom,r]] (*eigenvalues in diagonal matrix*) v=Orthogonalize@RandomVariate[NormalDistribution[], {r, r}](*orthonormal eigenvectors*) A=Transpose[v].eig.v Eigenvalues[A]

RandomVariate[NormalDistribution[], {r, r}] does not give you normalized eigenvectors. To obtain an orthonormal basis, you can first generate a random matrix, and then apply Orthogonalize to it. Following is the correct code.

r=4;(*matrix dimension*) dom={1,10};(*domain of random numbers*) eig=DiagonalMatrix[-RandomInteger[dom,r]] (*eigenvalues in diagonal matrix*) v=Orthogonalize@RandomVariate[NormalDistribution[], {r, r}](*orthonormal eigenvectors*) A=Transpose[v].eig.v Eigenvalues[A]
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Everett You
Everett You
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RandomVariate[NormalDistribution[], {r, r}] does not give you normalized eigenvectors. To obtain an orthonormal basis, you can first generate a random matrix, and then apply Orthogonalize to it. Following is the correct code.

r=4;(*matrix dimension*) dom={1,10};(*domain of random numbers*) eig=DiagonalMatrix[-RandomInteger[dom,r]] (*eigenvalues in diagonal matrix*) v=Orthogonalize@RandomReal[{-1,1}v=Orthogonalize@RandomVariate[NormalDistribution[], {r, r}](*orthonormal eigenvectors*) A=Transpose[v].eig.v Eigenvalues[A]

RandomVariate[NormalDistribution[], {r, r}] does not give you normalized eigenvectors. To obtain an orthonormal basis, you can first generate a random matrix, and then apply Orthogonalize to it. Following is the correct code.

r=4;(*matrix dimension*) dom={1,10};(*domain of random numbers*) eig=DiagonalMatrix[-RandomInteger[dom,r]] (*eigenvalues in diagonal matrix*) v=Orthogonalize@RandomReal[{-1,1},{r,r}](*orthonormal eigenvectors*) A=Transpose[v].eig.v Eigenvalues[A]

RandomVariate[NormalDistribution[], {r, r}] does not give you normalized eigenvectors. To obtain an orthonormal basis, you can first generate a random matrix, and then apply Orthogonalize to it. Following is the correct code.

r=4;(*matrix dimension*) dom={1,10};(*domain of random numbers*) eig=DiagonalMatrix[-RandomInteger[dom,r]] (*eigenvalues in diagonal matrix*) v=Orthogonalize@RandomVariate[NormalDistribution[], {r, r}](*orthonormal eigenvectors*) A=Transpose[v].eig.v Eigenvalues[A]
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Everett You
Everett You
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RandomVariate[NormalDistribution[], {r, r}] does not give you normalized eigenvectors. To obtain an orthonormal basis, you can first generate a random matrix, and then apply Orthogonalize to it. Following is the correct code.

r=4;(*matrix dimension*) dom={1,10};(*domain of random numbers*) eig=DiagonalMatrix[-RandomInteger[dom,r]] (*eigenvalues in diagonal matrix*) v=Orthogonalize@RandomReal[{-1,1},{r,r}](*orthonormal eigenvectors*) A=Transpose[v].eig.v Eigenvalues[A]