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When to use equivalence relations? How to write it in octave?

Dhamnekar Winod

Active member
Nov 17, 2018
161
Sometimes to help describe one expression, another expression is shown that produces identical results. The exact equivalence of expressions is indicated with ‘ ≡’.

For example: rot90 ([1, 2; 3, 4], -1) ≡ rot90 ([1, 2; 3, 4], 3) ≡ rot90 ([1, 2; 3, 4], 7)

What is the meaning of 'rot90;?

What is the meaning of this example?

How to write equivalence relation in octave?

How does all of the above expressions have equivalence relation?
 

Evgeny.Makarov

Well-known member
MHB Math Scholar
Jan 30, 2012
2,530
I don't know Octave, but rot90(x, k) probably is the result of rotating x by $k\cdot90^\circ$. I am not sure what [1, 2; 3, 4] represents: a matrix, points coordinates or something else, but this may not be important in this example. The important point is that rotating by $3\cdot90^\circ$ is the same as rotating by $7\cdot90^\circ$, which is also the same as rotating by $90^\circ$ in the opposite direction. Therefore, expressions rot90 ([1, 2; 3, 4], -1), rot90 ([1, 2; 3, 4], 3) and rot90 ([1, 2; 3, 4], 7) are equivalent. The set of all pairs of equivalent expressions forms an equivalence relation.