ランダム行列のランク確率は完全に1ですか？

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Ruby

2024/10/17

Is Probability of rank of random matrices is full 1?
I think of this in terms of measure of polynomials kernel space.If someone know about measurement probability, RMT or Argebrake geometry, let me know.

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なみだ

I don't think it makes sense to think about probability of rank of matrices because we can always get something from zero to up to the highest degree of the polynomial as a rank (so ultimately the probability is one), but idk[冷や汗] I do mathematics in university[にこやか]

2024/10/19 返信

Ruby

thankyou for your warm comment. I mean we can randomly choose full rank matrix where dimension is fixed.Of course this probability depends on a distribution you know. You can assume absolute continuous distribution if you need.But I couldn’t find good way to calculate the measure above.

なみだ

@Ruby ： thank you for your warm reply. We might assume the mean value and approximate the standard deviation of the distribution of rank of matrix with a fixed dimension through bootstraps method.

なみだ

@Ruby ： and therefore obtain a more specified distribution so we may calculate the probability of the kind you wish to get. I'm not sure if this helps, but it's nice to have a chat of this kind with somebody [にこやか]

Ruby

@なみだ： Thank you so much.

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