Let G be a square matrix, and
R =: |: (1&|."1) (=&i.) #G NB. rotation
M =: |: ( |."1) (=&i.) #G NB. mirror-image
dp =: +/ . *
Prove the following statement:
If
(1) G -: |:G NB. G is symmetric
(2) G -: R dp G dp |:R NB. G is rotationally symmetric
then
(3) G -: M dp G dp |:M NB. G is mirror-image symmetric
I can prove this using subscripts (i.e., involving
expressions like (<i;j){G ), but is there a proof
involving just the arrays G, R and M?
/John Wilson
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