matrix determinant

GolfScript, 58 chars

n%{~]}%{[.!{(.,,0\{:^2$=-1^?*3${.^<\^)>+}%d*+}/}or])\;}:d~

A straightforward recursive algorithm using Laplace expansion.

Example input (random 5 × 5 matrix):

-562   40   43 -586  347
-229  177  305 -367   50
-434  343  241 -365  -86
-3   -384 -351   61 -214
-400   96 -339   25 -116

Output: 282416596900 (Online demo; Verify with Wolfram Alpha)

The code consists of three parts:

• n%{~]}% parses the input,
• {[.!{(.,,0\{:^2$=-1^?*3${.^<\^)>+}%d*+}/}or])\;}:d defines a recursive subroutine to calculate the determinant, and
• the final ~ applies the subroutine to the input.

I'm sure there's room for improvement in this code, but at least I beat Gareth by three chars. Also, {:^2$= is a pretty nice GS smiley. :)

Haskell, 139 131

(a:r)%0=r;(a:r)%n=a:r%(n-1)
d[]=1;d(f:r)=foldr(\(j,x)->(x*d(map(%j)r)-))0$zip[0..]f
main=interact$show.d.map(map read.words).lines

Python 233

def d(x):
 l=len(x)
 if l<2:return x[0][0]
 return sum([(-1)**i*x[i][0]*d(m(x,i))for i in range(l)])
def m(x,i):y=x[:];del(y[i]);y=zip(*y);del(y[0]);return zip(*y)
x=[input()]
for i in (len(x[0])-1)*[1]:x+=[input()]
print d(x)

Ungolfed:

def det(x):
    l = len(x)
    if l == 1:
        return x[0][0]
    return sum([(-1)**i*x[i][0]*det(minor(x,i+1,1)) for i in range(l)])

def minor(x,i,j):
    y = x[:]
    del(y[i-1])
    y=zip(*y)
    del(y[j-1])
    return zip(*y)

def main():
    x = [input()]
    for i in range(len(x[0])-1):
        x += [input()]
    print det(x)

if __name__ == '__main__':
    main()

Usage

As requested, input is on stdin and output is to stdout.

I interpreted columns separated by any space char to mean that I can use comma delimited numbers. If this is not the case, I will rework my solution.

This could be about 30 characters shorter if I could specify my input matrix in the form [[a,b,c],[d,e,f],[g,h,i]].

./det.py
1,-4,9
-6,7,3
1,2,3

Result

-240

The determinant is found using Laplace Expansion