File:Walsh permutation 124 JF.png

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The square matrix above is the transformation matrix used. Below it are the coordinates of the initial cube and those of the transformed cube shown in this image. In a matrix multiplication the matrix is multiplied from the left, and the coordinates are column vectors.


The tables on the right show the same coordinates, but formatted to be read as those of the orthographic projections. Those marked with a darker frame are the ones shown in the 3D image. (Also their axes are in alphabetic order, which makes them more intuitive to read.)

(−1, −1, −1) (1, −1, −1) (−1, 1, −1) (1, 1, −1) (−1, −1, 1) (1, −1, 1) (−1, 1, 1) (1, 1, 1)


124
+1±0±0
±0+1±0
±0±0+1
 +x
 +y
 +z
  
&0 −1−1−1&0 −1−1−1
&1 +1−1−1&1 +1−1−1
&2 −1+1−1&2 −1+1−1
&3 +1+1−1&3 +1+1−1
&4 −1−1+1&4 −1−1+1
&5 +1−1+1&5 +1−1+1
&6 −1+1+1&6 −1+1+1
&7 +1+1+1&7 +1+1+1
xyz
−1−1−1−1−1−1
+1−1−1+1
−1+1−1−1+1−1
+1+1−1+1
−1−1+1−1−1+1
+1−1+1+1
−1+1+1−1+1+1
+1+1+1+1
xyz
−1−1−1−1−1−1
−1+1−1+1
+1−1−1+1−1−1
+1+1−1+1
−1−1+1−1−1+1
−1+1+1+1
+1−1+1+1−1+1
+1+1+1+1
xyz
−1−1−1−1−1−1
−1−1+1+1
+1−1−1+1−1−1
+1−1+1+1
−1+1−1−1+1−1
−1+1+1+1
+1+1−1+1+1−1
+1+1+1+1
−x
−y
−z

Summary

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Description

This is an example object to illustrate linear tranformations. In this case the tranformation matrix is the identity, so the object is unchanged.

Related images of Walsh permutation 124
part of Related sets of 3-bit Walsh permutations
Source Own work
Author
Watchduck
You can name the author as "T. Piesk", "Tilman Piesk" or "Watchduck".
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current00:02, 28 December 2021Thumbnail for version as of 00:02, 28 December 20214,000 × 3,880 (710 KB)Watchduck (talk | contribs)uploaded with Pywikibot

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