The function Minors[] does not return what its suposse to. Example:

mat = {{a, b, c}, {l, m, n}, {x, y, z}}
mat // MatrixForm
Minors[mat] // MatrixForm

The output for minors is :

{{-b l + a m, -c l + a n, -c m + b n}, {-b x + a y, -c x + a z, -c y +
    b z}, {-m x + l y, -n x + l z, -n y + m z}}

It calculates all the minors but places them in wrong possitions. Minor for possition 1,1 is in position 3,3. On symbolab it calculates it correctly. Am i not using the correct function? What am i missing here?

enter image description here

  • 2
    $\begingroup$ Indeed, Minors does not what one usually expects. Please read the documentation of Minors more carefully, in particular the "Details" section. $\endgroup$ Apr 29 '20 at 10:52
  • 1
    $\begingroup$ The output is consistent with the documentation of Minors, see first point of Details. I agree it's not the definition I know either though. $\endgroup$
    – anderstood
    Apr 29 '20 at 10:53
  • 1
    $\begingroup$ You could always 'roll your own': Table[Det@Drop[mat, {i},{j}], {i,3},{j,3}]//MatrixForm. Also, this post by Carl Woll might be of interest. $\endgroup$
    – user1066
    Apr 29 '20 at 13:56
  • 1
    $\begingroup$ From the documentation, Map[Reverse, Minors[mat], {0,1}] may be what you are looking for? And: Map[Reverse, Minors[mat], {0,1}]==Table[Det@Drop[mat, {i},{j}], {i,3},{j,3}] $\endgroup$
    – user1066
    Apr 29 '20 at 22:09

You can get the more natural order by post-processing

(mat = {{a, b, c}, {l, m, n}, {x, y, z}}) // MatrixForm

Mathematica graphics

min = Minors[mat];
(Reverse[min, {1, 2}]) // MatrixForm

Mathematica graphics


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