Binary Matrix Rank (GF(2))
HardMatrixMathBit Manipulation
Description
Given a matrix of 0s and 1s, return its rank over the field GF(2) (i.e., arithmetic modulo 2 via Gaussian elimination using XOR).
Examples
Input:
matrix = [[1,0],[0,1]]Output:
2Explanation:
Identity has full rank 2.
Input:
matrix = [[1,1],[1,1]]Output:
1Explanation:
Rows linearly dependent.
Input:
matrix = [[1,0,1],[0,1,1],[1,1,0]]Output:
2Explanation:
Third row equals XOR of first two.
Constraints
- •
1 ≤ rows, cols ≤ 30 - •
matrix[i][j] ∈ {0, 1}