gfrank

R2026b

Compute rank of matrix over Galois field

Syntax

rk = gfrank(A,)

rk = gfrank(A,p)

Description

rk = gfrank(A,) calculates the rank of matrix A for GF(2).

rk = gfrank(A,p) calculates the rank of matrix A for GF(p), where p is a prime number.

Examples

Find Rank of Matrix of GF(3)

Define a 3-by-3 matrix A.

A = [1 0 1;
    2 1 0;
    0 1 1];

Define the prime number or the GF(p).

p = 3;

Compute the ordinary determinant of matrix A.

det_a = det(A);  

Take the determinant modulo p or determinant in GF(3).

detmodp = rem(det(A),p);

Compute the rank of matrix A over GF(3) using modulo arithmetic.

rankp = gfrank(A,p);

Display the results.

disp(['Determinant = ',num2str(det_a)])

Determinant = 3

disp(['Determinant mod p is ',num2str(detmodp)])

Determinant mod p is 0

disp(['Rank over GF(p) is ',num2str(rankp)])

Rank over GF(p) is 2

Input Arguments

A — Input matrix

matrix of integers

Input matrix, specified as a matrix of integers.

Data Types: double

p — Prime number

2 (default) | scalar

Prime number, specified as a scalar. Each entry in a and b represents an element of GF(p). The entries of a and b are integers in the range [0, (p – 1)].

Data Types: double

Output Arguments

rk — Rank of the matrix A

positive integer

Rank of the matrix A, returned as a positive integer.

Data Types: double

Tips

• This function performs computations in GF(p^m) where p is a prime number. If you are working in GF(2^m), use the rank function with Galois arrays. For details, see Computing Ranks.

Algorithms

gfrank uses an algorithm similar to Gaussian elimination.

Version History

Introduced before R2006a