Skip to main content

linear algebra - Difference In Eigenvectors


When running my program in both Mathematica and MathCad, I end up with the same eigenvalues, but different eigenvectors. The ones in MathCad are normalized, which the documentation for Mathematica says they too are normalized. I also tried Normalize[] and they still differed. Any advice for how to change it so that they match up?


EDIT:: Code



{{0. + 0. I, -0.00105652 + 0.00306633 I, -0.000992072 - 0.000550179 I,
   0. + 0. I, 0. + 0. I, 0. + 0. I, 0. + 0. I, 0. + 0. I, 0. + 0. I, 
  0. + 0. I, 0. + 0. I, -0.00080248 - 0.000276499 I, 
  3.94975*10^-6 - 7.12212*10^-6 I, 
  0.0000192495 + 6.63251*10^-6 I, -7.8995*10^-6 + 
   0.0000142442 I, -2.53122*10^-6 - 2.0506*10^-6 I, 0. + 0. I, 
  0. + 0. I, 0. + 0. I, 0. + 0. I, 0. + 0. I, 
  0. + 0. I}, {0.00119848 - 0.00323969 I, 
  0. + 0. I, -0.00089753 + 0.00242618 I, -0.000743608 - 0.000434551 I,
   0. + 0. I, 0. + 0. I, 0. + 0. I, 0. + 0. I, 0. + 0. I, 0. + 0. I, 

  0. + 0. I, -1.5511*10^-6 + 8.53409*10^-6 I, -0.000868186 - 
   0.000321173 I, 8.75277*10^-6 - 0.0000149778 I, 
  0.0000203377 + 7.52365*10^-6 I, -8.75277*10^-6 + 
   0.0000149778 I, -2.64607*10^-6 - 2.24413*10^-6 I, 0. + 0. I, 
  0. + 0. I, 0. + 0. I, 0. + 0. I, 
  0. + 0. I}, {-0.00124465 - 0.00025056 I, 0.000991057 - 0.00253121 I,
   0. + 0. I, -0.000658751 + 0.00168248 I, -0.000461387 - 
   0.000281434 I, 0. + 0. I, 0. + 0. I, 0. + 0. I, 0. + 0. I, 
  0. + 0. I, 0. + 0. I, 
  0.0000212182 + 8.30765*10^-6 I, -3.59755*10^-6 + 

   0.0000178707 I, -0.000909167 - 0.00035597 I, 
  9.49275*10^-6 - 0.0000155626 I, 
  0.0000212182 + 8.30765*10^-6 I, -9.49275*10^-6 + 
   0.0000155626 I, -2.73555*10^-6 - 2.41019*10^-6 I, 0. + 0. I, 
  0. + 0. I, 0. + 0. I, 
  0. + 0. I}, {0. + 0. I, -0.000915438 - 0.000197309 I, 
  0.000705296 - 0.00173145 I, 
  0. + 0. I, -0.00034951 + 0.000858025 I, -0.000154043 - 
   0.0000968679 I, 0. + 0. I, 0. + 0. I, 0. + 0. I, 0. + 0. I, 
  0. + 0. I, 3.97422*10^-6 - 0.0000184388 I, 

  0.0000218358 + 8.89464*10^-6 I, -3.97422*10^-6 + 
   0.0000184388 I, -0.000935629 - 0.000381122 I, 
  0.000010041 - 0.0000159676 I, 
  0.0000218358 + 8.89464*10^-6 I, -0.000010041 + 
   0.0000159676 I, -2.79628*10^-6 - 2.53224*10^-6 I, 0. + 0. I, 
  0. + 0. I, 0. + 0. I}, {0. + 0. I, 
  0. + 0. I, -0.000555325 - 0.000123831 I, 
  0.000361803 - 0.000870433 I, 0. + 0. I, 
  6.4961*10^-6 - 0.0000156284 I, 0.000167434 + 0.000106958 I, 
  0. + 0. I, 0. + 0. I, 0. + 0. I, 

  0. + 0. I, -3.83436*10^-6 - 1.7215*10^-7 I, 
  4.17683*10^-6 - 0.0000187311 I, 
  0.0000221515 + 9.20749*10^-6 I, -4.17683*10^-6 + 
   0.0000187311 I, -0.000949159 - 0.000394527 I, 
  0.0000103313 - 0.0000161729 I, 
  0.0000221515 + 9.20749*10^-6 I, -0.0000103313 + 
   0.0000161729 I, -2.82664*10^-6 - 2.59656*10^-6 I, 0. + 0. I, 
  0. + 0. I}, {0. + 0. I, 0. + 0. I, 
  0. + 0. I, -0.000180652 - 0.0000402588 I, -6.49204*10^-6 + 
   0.0000156244 I, 0. + 0. I, 0.000374561 - 0.000901456 I, 

  0.00049078 + 0.000313423 I, 0. + 0. I, 0. + 0. I, 0. + 0. I, 
  0. + 0. I, -3.83319*10^-6 - 1.71599*10^-7 I, 
  4.17309*10^-6 - 0.0000187258 I, 
  0.0000221458 + 9.20173*10^-6 I, -4.17309*10^-6 + 
   0.0000187258 I, -0.000948914 - 0.00039428 I, 
  0.000010326 - 0.0000161692 I, 
  0.0000221458 + 9.20173*10^-6 I, -0.000010326 + 
   0.0000161692 I, -2.82609*10^-6 - 2.59538*10^-6 I, 
  0. + 0. I}, {0. + 0. I, 0. + 0. I, 0. + 0. I, 0. + 0. I, 
  0.000190732 + 0.0000410344 I, -0.000361392 + 0.000888151 I, 

  0. + 0. I, 0.000716521 - 0.00176091 I, 0.00080346 + 0.000504823 I, 
  0. + 0. I, 0. + 0. I, 0. + 0. I, 
  0. + 0. I, -3.76634*10^-6 - 1.40845*10^-7 I, 
  3.96361*10^-6 - 0.0000184233 I, 
  0.0000218189 + 8.87822*10^-6 I, -3.96361*10^-6 + 
   0.0000184233 I, -0.000934908 - 0.000380418 I, 
  0.0000100257 - 0.0000159566 I, 
  0.0000218189 + 8.87822*10^-6 I, -0.0000100257 + 
   0.0000159566 I, -2.79465*10^-6 - 2.52885*10^-6 I}, {0. + 0. I, 
  0. + 0. I, 0. + 0. I, 0. + 0. I, 0. + 0. I, 

  0.000541679 + 0.000108715 I, -0.00066847 + 0.00171026 I, 0. + 0. I, 
  0.000999783 - 0.00255791 I, 0.00109362 + 0.000666203 I, 0. + 0. I, 
  0. + 0. I, 0. + 0. I, 0. + 0. I, -3.63939*10^-6 - 8.56735*10^-8 I, 
  3.58173*10^-6 - 0.0000178461 I, 
  0.0000211913 + 8.28283*10^-6 I, -3.58173*10^-6 + 
   0.0000178461 I, -0.000908015 - 0.000354907 I, 
  9.46946*10^-6 - 0.0000155449 I, 
  0.0000211913 + 8.28283*10^-6 I, -9.46946*10^-6 + 
   0.0000155449 I}, {0. + 0. I, 0. + 0. I, 0. + 0. I, 0. + 0. I, 
  0. + 0. I, 0. + 0. I, 

  0.000857822 + 0.000155255 I, -0.000904508 + 0.00245062 I, 0. + 0. I,
   0.00120425 - 0.00326273 I, 0.00135116 + 0.000788249 I, 0. + 0. I, 
  0. + 0. I, 0. + 0. I, 0. + 0. I, -3.46257*10^-6 - 1.56372*10^-8 I, 
  3.08334*10^-6 - 0.0000170362 I, 
  0.0000203025 + 7.49351*10^-6 I, -3.08334*10^-6 + 
   0.0000170362 I, -0.000869931 - 0.000321086 I, 
  8.72413*10^-6 - 0.0000149543 I, 
  0.0000203025 + 7.49351*10^-6 I}, {0. + 0. I, 0. + 0. I, 0. + 0. I, 
  0. + 0. I, 0. + 0. I, 0. + 0. I, 0. + 0. I, 
  0.00112915 + 0.000178104 I, -0.00106069 + 0.00308684 I, 0. + 0. I, 

  0.0013247 - 0.00385516 I, 0. + 0. I, 0. + 0. I, 0. + 0. I, 
  0. + 0. I, 0. + 0. I, -3.24913*10^-6 + 5.87823*10^-8 I, 
  2.53158*10^-6 - 0.0000160499 I, 
  0.0000192081 + 6.60019*10^-6 I, -2.53158*10^-6 + 
   0.0000160499 I, -0.000819963 - 0.000281752 I, 
  3.93415*10^-6 - 7.10805*10^-6 I}, {0. + 0. I, 0. + 0. I, 0. + 0. I, 
  0. + 0. I, 0. + 0. I, 0. + 0. I, 0. + 0. I, 0. + 0. I, 
  0.00135075 + 0.000179137 I, -0.00114114 + 0.00360727 I, 0. + 0. I, 
  0. + 0. I, 0. + 0. I, 0. + 0. I, 0. + 0. I, 0. + 0. I, 
  0. + 0. I, -3.01338*10^-6 + 1.28696*10^-7 I, 

  1.98264*10^-6 - 0.0000149497 I, 
  0.0000179729 + 5.68564*10^-6 I, -9.91319*10^-7 + 
   7.47487*10^-6 I, -0.000749264 - 0.000237026 I}, {1, 0, 0, 0, 0, 0, 
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 0, 
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 0, 
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 1, 
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 
  1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 

  0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 
  0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 
  0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 
  0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}}

I will work on getting the MathCad, but the first few values of the 19th eigenvector should be -.001048-.001033i, -.002461-.00404i...




Comments

Post a Comment

Popular posts from this blog

plotting - How to draw lines between specified dots on ListPlot?

I would like to create a plot where I have unconnected dots and some connected. So far, I have figured out how to draw the dots. My code is the following: ListPlot[{{1, 1}, {2, 2}, {3, 3}, {4, 4}, {1, 4}, {2, 5}, {3, 6}, {4, 7}, {1, 7}, {2, 8}, {3, 9}, {4, 10}, {1, 10}, {2, 11}, {3, 12}, {4,13}, {2.5, 7}}, Ticks -> {{1, 2, 3, 4}, None}, AxesStyle -> Thin, TicksStyle -> Directive[Black, Bold, 12], Mesh -> Full] I have thought using ListLinePlot command, but I don't know how to specify to the command to draw only selected lines between the dots. Do have any suggestions/hints on how to do that? Thank you. Answer One possibility would be to use Epilog with Line : ListPlot[ {{1, 1}, {2, 2}, {3, 3}, {4, 4}, {1, 4}, {2, 5}, {3, 6}, {4, 7}, {1, 7}, {2, 8}, {3, 9}, {4, 10}, {1, 10}, {2, 11}, {3, 12}, {4, 13}, {2.5, 7}}, Ticks -> {{1, 2, 3, 4}, None}, AxesStyle -> Thin, TicksStyle -> Directive[Black, Bold, 12], Mesh -> Full, Epilog -> { Line[ ...
Post a Comment
Read more

dynamic - How can I make a clickable ArrayPlot that returns input?

I would like to create a dynamic ArrayPlot so that the rectangles, when clicked, provide the input. Can I use ArrayPlot for this? Or is there something else I should have to use? Answer ArrayPlot is much more than just a simple array like Grid : it represents a ranged 2D dataset, and its visualization can be finetuned by options like DataReversed and DataRange . These features make it quite complicated to reproduce the same layout and order with Grid . Here I offer AnnotatedArrayPlot which comes in handy when your dataset is more than just a flat 2D array. The dynamic interface allows highlighting individual cells and possibly interacting with them. AnnotatedArrayPlot works the same way as ArrayPlot and accepts the same options plus Enabled , HighlightCoordinates , HighlightStyle and HighlightElementFunction . data = {{Missing["HasSomeMoreData"], GrayLevel[ 1], {RGBColor[0, 1, 1], RGBColor[0, 0, 1], GrayLevel[1]}, RGBColor[0, 1, 0]}, {GrayLevel[0], GrayLevel...
Post a Comment
Read more

list manipulation - Selecting multiple columns from a matrix?

Sample data: data = { {{2013, 1, 1}, 24.13, 167.67, 231.82}, {{2013, 1, 2}, 32.15, 170.92, 225.99}, {{2013, 1, 3}, 35.43, 172.68, 221.67}, {{2013, 1, 4}, 36.73, 173.05, 218.32}, {{2013, 1, 5}, 58.19, 165.96, 197.05}, {{2013, 1, 6}, 69.99, 163.50, 187.52}, {{2013, 1, 7}, 71.37, 154.21, 175.58}, {{2013, 1, 8}, 72.51, 149.66, 163.25}}; I want a DateListPlot with three graphs, so for a matrix formed by columns 1 and 2, one for columns 1 and 3, and 1 for columns 1 and 4. At the moment I'm using this code: data2 = Transpose[{data[[All, 1]], data[[All, 2]]}]; data3 = Transpose[{data[[All, 1]], data[[All, 3]]}]; data4 = Transpose[{data[[All, 1]], data[[All, 4]]}]; DateListPlot[{data2, data3, data4}, Joined -> True, Filling -> {3 -> {1}}] but I have a hunch that this can be done more efficiently. I don't like the Transpose s in particular. Any ideas? edit (for extra credit) What if I need to multiply the second column by 2, which in my solution is simp...
Post a Comment
Read more