# Algorithm Implementation/Mathematics/Determinant of a Matrix

```--Takes input with the matrix as a list of rows, throws an error if the list isn't square
--This probably isn't the most elegant/efficient way to do it, but it's something
alternatingSum :: Num a => [a] -> a
alternatingSum [] = 0
alternatingSum l  = iter l 0 0
where iter (x:xs) n result = if even n then iter xs (n + 1) (result + x) else iter xs (n + 1) (result - x)
iter [] _ result = result

removeColumn :: Int -> [[a]] -> [[a]]
removeColumn n = map (removeIndex n)

removeIndex :: Int -> [a] -> [a]
removeIndex 0 (x:xs) = xs
removeIndex n (x:xs) = x : removeIndex (n-1) xs
removeIndex _ []     = []

isSquare :: [[a]] -> Bool
isSquare (row:rows) = and \$ map eqFirstLength rows
where l = length row
eqFirstLength list = length list == l
isSquare [] = True

determinant :: Num a => [[a]] -> a
determinant matrix
| isSquare matrix   = helper matrix
| otherwise         = error "DETERMINANT --> MATRIX IS NOT SQUARE"
where helper [[x1,x2],[y1,y2]] = x1 * y2 - x2 * y1
helper (x:xs)            = let l = length x in alternatingSum \$ zipWith (*) x \$ map (\n -> determinant \$ removeColumn n xs) [0..l]
helper [] = 0
```

## Java

```       public static double[][] reduce(double[][] x, double[][] y, int r, int c, int n)
{
for (int h = 0, j = 0; h < n; h++)
{
if (h == r)
continue;
for (int i = 0, k = 0; i < n; i++)
{
if (i == c)
continue;
y[j][k] = x[h][i];
k++;
} //end inner loop
j++;
} //end outer loop
return y;
} //end method
//===================================================
public static double det(int NMAX, double[][] x)
{
double ret=0;
if (NMAX < 4)//base case
{
double prod1=1, prod2=1;
for (int i = 0; i < NMAX; i++)
{
prod1=1;
prod2=1;

for (int j = 0; j < NMAX; j++)
{
prod1 *= x[(j + i + 1) % NMAX][j];
prod2 *= x[(j + i + 1) % NMAX][NMAX - j - 1];
} //end inner loop
ret += prod1 - prod2;
} //end outer loop
return ret;
} //end base case
double[][] y = new double [NMAX - 1][NMAX - 1];
for (int h = 0; h < NMAX; h++)
{
if (x[h][0] == 0)
continue;
reduce(x, y, h, 0, NMAX);
if (h % 2 == 0) ret -= det(NMAX - 1, y) * x[h][0];
if (h  %2 == 1) ret += det(NMAX - 1, y) * x[h][0];
} //end loop
return ret;
} //end method
```