1 * X' * X is not symmetric

[Tamas_Papp]

@e3c6

I want to understand where it comes from to understand the kind of floating point errors I might be committing here.

A good starting point would be

PSA: floating-point arithmetic

Sometimes people are surprised by the results of floating-point calculations such as julia> 5/6 0.8333333333333334 # shouldn't the last digit be 3? julia> 2.6 - 0.7 - 1.9 2.220446049250313e-16 # shouldn't the answer be 0? These are not bugs in Julia. They’re consequences of the IEEE-standard 64-bit binary representation of floating-point numbers that is burned into computer hardware, which Julia and many other languages use by default. Brief explanation You can t…

TL;DR: order matters, if you know (from theory) that two things are equal and want to use it like that, don’t calculate it twice, or discard one of them. Hence Symmetric.