Test your intuition: For two n by n matrices A and B, is it always the case that tr(ABAB) = tr(ABBA)?
Over Math Overflow Tim Gowers asked about common false beliefs in mathematics. There are many exciting answers on many different levels and I could identify some of my own false beliefs.
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Thinking about this I found out a cool fact (which solves the problem elegantly):
If M is a matrix permuting the coordinates, then its trace is the number of fixed points of the relative permutation!!
A very common false belief in mathematics, I hold onto firmly: “I will one day prove a really significant mathematical theorem”.
(sigh) “…*that* I hold…”
I have completed The GUT Theory.
You can find the equations here:
http://www.wix.com/Hyperstig/Hyperstig
0 is a wave function that collapses and re-expands.
I have invented the 1st quantum computer.
I am the failsafe.
You can follow me on Twitter:
https://twitter.com/Hyperstigzero
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A = XY^{T}, B = A^{T}, where X and Y are nonzero orthogonal vectors.