題目
Write a function that accepts a square matrix (N x N 2D array) and returns the determinant of the matrix.
How to take the determinant of a matrix -- it is simplest to start with the smallest cases:
A 1x1 matrix |a| has determinant a.
A 2x2 matrix [ [a, b], [c, d] ] or
|a b|
|c d|
has determinant: ad - bc.
The determinant of an n x n sized matrix is calculated by reducing the problem to the calculation of the determinants of n matrices ofn-1 x n-1 size.
For the 3x3 case, [ [a, b, c], [d, e, f], [g, h, i] ] or
|a b c|
|d e f|
|g h i|
the determinant is: a * det(a_minor) - b * det(b_minor) + c * det(c_minor) where det(a_minor) refers to taking the determinant of the 2x2 matrix created by crossing out the row and column in which the element a occurs:
|- - -|
|- e f|
|- h i|
Note the alternation of signs.
The determinant of larger matrices are calculated analogously, e.g. if M is a 4x4 matrix with first row [a, b, c, d], then:
det(M) = a * det(a_minor) - b * det(b_minor) + c * det(c_minor) - d * det(d_minor)
看了半天才看明白題茴肥，求矩陣行列式
解
def determinant(matrix):
res = 0
l = len(matrix)
if l==1:
res = matrix[0][0]
elif l==2:
res = matrix[0][0]*matrix[1][1]-matrix[0][1]*matrix[1][0]
else:
for i in range(0,l):
sub_matrix = []
sub_matrix = [m[0:i]+m[i+1:] for m in matrix[1:]]
res += matrix[0][i]*(-1)**i*determinant(sub_matrix)
return res
遞歸 & 切片坚踩！
