# Algorithm Implementation/Linear Algebra/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
```

## Java

```public int determinant(int[][] m) {
int n = m.length;
if(n == 1) {
return m[0][0];
} else {
int det = 0;
for(int j = 0; j < n; j++) {
det += Math.pow(-1, j) * m[0][j] * determinant(minor(m, 0, j));
}
return det;
}
}

public int[][] minor(final int[][] m, final int i, final int j) {
int n = m.length;
int[][] minor = new int[n - 1][n - 1];
int r = 0, s = 0;
for(int k = 0; k < n; k++) {
int[] row = m[k];
if(k != i) {
for(int l = 0; l < row.length; l++) {
if(l != j) {
minor[r][s++] = row[l];
}
}
r++;
s = 0;
}
}
return minor;
}
```

## Phix

```function minor(sequence a, integer x, integer y)
integer l = length(a)-1
sequence result = repeat(repeat(0,l),l)
for i=1 to l do
for j=1 to l do
result[i][j] = a[i+(i>=x)][j+(j>=y)]
end for
end for
return result
end function

function det(sequence a)
if length(a)=1 then
return a[1][1]
end if
integer sgn = 1
integer res = 0
for i=1 to length(a) do
res += sgn*a[1][i]*det(minor(a,1,i))
sgn *= -1
end for
return res
end function
```