Quickly find the rank of any matrix (m x n) using our free Matrix Rank Calculator. Understand linear independence, the dimension of the column space, and how it relates to the nullity of a matrix with ease. Perfect for students and professionals in linear algebra and data science.
Formula:
The rank of a matrix A, denoted as rank(A), is the maximum number of linearly independent column vectors in the matrix. Equivalently, it is the maximum number of linearly independent row vectors. It represents the dimension of the column space (or row space).
To calculate the rank, the most common method involves transforming the matrix into its row echelon form (or reduced row echelon form) using elementary row operations and then counting the number of non-zero rows. Each non-zero row after row reduction corresponds to a pivot element, indicating a linearly independent vector.