Matrix Rank Calculator
Find the rank of any matrix using row reduction.
How It Works
Enter any matrix. The calculator applies Gaussian elimination to reduce the matrix to row echelon form and counts the number of non-zero rows, which equals the rank.
Formula
Rank = number of non-zero rows in row echelon form
Frequently Asked Questions
What is matrix rank?
The rank of a matrix is the number of linearly independent rows (or columns). It equals the dimension of the row space and the column space.
What is full rank?
A matrix is full rank when its rank equals the smaller of the number of rows and columns — meaning all rows or columns are linearly independent.