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J. M.'s missing motivation ♦
J. M.'s missing motivation ♦
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It seems to have been missed that NullSpace[] is a built-in function:

mat = {{9, -48, 4}, {36, 4, -33}, {32, 9, 36}}/49;

evs = Eigenvalues[mat]
   {I, -I, 1}

NullSpace[mat - # IdentityMatrix[3]]IdentityMatrix[Length[mat]]] & /@ evs
   {{{-(18/13) + (14 I)/13, 12/13 + (21 I)/13, 1}},
    {{-(18/13) - (14 I)/13, 12/13 - (21 I)/13, 1}},
    {{1/2, -(1/3), 1}}}

Since NullSpace[] returns a list of vectors instead of a single vector (as it should), one might want to execute Flatten[%, 1] afterwards to get the eigenvectors as a list of vectors. Note that the result in this case matches the output of Eigenvectors[mat].

It seems to have been missed that NullSpace[] is a built-in function:

mat = {{9, -48, 4}, {36, 4, -33}, {32, 9, 36}}/49;

evs = Eigenvalues[mat]
   {I, -I, 1}

NullSpace[mat - # IdentityMatrix[3]] & /@ evs
   {{{-(18/13) + (14 I)/13, 12/13 + (21 I)/13, 1}},
    {{-(18/13) - (14 I)/13, 12/13 - (21 I)/13, 1}},
    {{1/2, -(1/3), 1}}}

Since NullSpace[] returns a list of vectors instead of a single vector (as it should), one might want to execute Flatten[%, 1] afterwards to get the eigenvectors as a list of vectors. Note that the result in this case matches the output of Eigenvectors[mat].

It seems to have been missed that NullSpace[] is a built-in function:

mat = {{9, -48, 4}, {36, 4, -33}, {32, 9, 36}}/49;

evs = Eigenvalues[mat]
   {I, -I, 1}

NullSpace[mat - # IdentityMatrix[Length[mat]]] & /@ evs
   {{{-18/13 + 14 I/13, 12/13 + 21 I/13, 1}},
    {{-18/13 - 14 I/13, 12/13 - 21 I/13, 1}},
    {{1/2, -1/3, 1}}}

Since NullSpace[] returns a list of vectors instead of a single vector (as it should), one might want to execute Flatten[%, 1] afterwards to get the eigenvectors as a list of vectors. Note that the result in this case matches the output of Eigenvectors[mat].

Source Link
J. M.'s missing motivation ♦
J. M.'s missing motivation ♦
  • 125.5k
  • 11
  • 407
  • 581

It seems to have been missed that NullSpace[] is a built-in function:

mat = {{9, -48, 4}, {36, 4, -33}, {32, 9, 36}}/49;

evs = Eigenvalues[mat]
   {I, -I, 1}

NullSpace[mat - # IdentityMatrix[3]] & /@ evs
   {{{-(18/13) + (14 I)/13, 12/13 + (21 I)/13, 1}},
    {{-(18/13) - (14 I)/13, 12/13 - (21 I)/13, 1}},
    {{1/2, -(1/3), 1}}}

Since NullSpace[] returns a list of vectors instead of a single vector (as it should), one might want to execute Flatten[%, 1] afterwards to get the eigenvectors as a list of vectors. Note that the result in this case matches the output of Eigenvectors[mat].