Revisions to What is the best way to compute the set of vectors normal to a given one?

deleted 28 characters in body

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edited Nov 25, 2018 at 14:31

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general solution

normalVecs[vec_] := 
Cross[vec, ## & @@Module[{l #]= &Length@vec}, 
Cross[vec,##&@@#]&/@ 
Subsets[IdentityMatrix[Length@vec]Subsets[IdentityMatrix@l, {Length@vec l- 2}] // 
DeleteCases@Table[0, Length@vec]   l]]  


normalVecs[{1, 0, 0, 0, 0, 0}]

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

general solution

normalVecs[vec_] := 
Cross[vec, ## & @@ #] & /@ 
Subsets[IdentityMatrix[Length@vec], {Length@vec - 2}] // 
DeleteCases@Table[0, Length@vec]     


normalVecs[{1, 0, 0, 0, 0, 0}]

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

general solution

normalVecs[vec_] := Module[{l = Length@vec}, 
Cross[vec,##&@@#]&/@ Subsets[IdentityMatrix@l,{l-2}] //DeleteCases@Table[0,l]]  


normalVecs[{1, 0, 0, 0, 0, 0}]

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

added 151 characters in body

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edited Nov 25, 2018 at 14:21

ZaMoC

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13
32

how is this for 4D?general solution

Cross[{1,0,0,0}normalVecs[vec_] := 
Cross[vec,##&@@#]& ## & @@ #] & /@ Subsets[IdentityMatrix@4
Subsets[IdentityMatrix[Length@vec], {Length@vec - 2}] // DeleteCases@
DeleteCases@Table[0, Length@vec]     


normalVecs[{1, 0, 0, 0, 0, 0}]

{{0, 00, 00, 10,0,1}, {0, 00, 0,0,-1, 00}, {0, 10, 00, 01,0,0},{0,0,-1,0,0,0},{0,1,0,0,0,0}}

how is this for 4D?

Cross[{1,0,0,0},##&@@#]&/@ Subsets[IdentityMatrix@4,{2}]// DeleteCases@{0,0,0,0}

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

general solution

normalVecs[vec_] := 
Cross[vec, ## & @@ #] & /@ 
Subsets[IdentityMatrix[Length@vec], {Length@vec - 2}] // 
DeleteCases@Table[0, Length@vec]     


normalVecs[{1, 0, 0, 0, 0, 0}]

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

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created Nov 25, 2018 at 14:15

ZaMoC

6.8k
13
32

how is this for 4D?

Cross[{1,0,0,0},##&@@#]&/@ Subsets[IdentityMatrix@4,{2}]// DeleteCases@{0,0,0,0}

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

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