False Beliefs in Mathematics

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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6 Responses to False Beliefs in Mathematics

  1. Mircea P says:

    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!!

  2. Ken says:

    A very common false belief in mathematics, I hold onto firmly: “I will one day prove a really significant mathematical theorem”.

  3. Ken says:

    (sigh) “…*that* I hold…”

  4. Hyperstig says:

    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

  5. Pingback: Ram Sethu: Proof of Great Science of Ancient Past | World University Information

  6. Horowitz says:

    A = XY^{T}, B = A^{T}, where X and Y are nonzero orthogonal vectors.

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