Re: Inverse Matrix Function appears a bit wonky

[Mike Miller]

On Fri, 5 Nov 2004, Przemek Klosowski wrote:

> OK, the official results are in: 3x3 {0..9}-valued matrices it's 4%, and 
> 2% for 4x4 matrices, and .5% for 5x5 matrices. Funny. The originator of 
> this thread had 1-in-60 chance of picking a singular matrix.

I can tell you one thing for certain - people aren't good at generating 
random numbers (my PhD is in psychology and this is a topic we 
occasionally discuss).  Anyway, it seems like people will often try to 
make a 4x4 matrix and they'll start with something like this:

1 1
1 2
1 3
1 4

If they start with that, and have to use only integers 1-4 for the 
remaining two columns, then what are their chances of getting a singular 
matrix?  (Assume they can choose numbers randomly, even though they 
can't.)  I think the probability is much higher than 4%.  The human 
tendency toward nonrandomness is what throws things off.

By the way, the classic example of human inability to generate random 
patterns is seen when you ask people to generate a series of mental coin 
tosses.  They tend not to give you strings of 5 or 6 consecutive heads and 
they give you too much alternation: HTHTHT.  But HHHHHH and HTHTHT have 
the same probability.  It can make a fun classroom presentation.

Mike



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