Matrix Rank Calculator

Matrix Rank Calculator

Find the rank of a matrix by reducing it to row-echelon form and counting pivot rows.

Last updated: June 2026 | By Patchworkr Team

Matrix Rank Solver
Matrix Rank
0
The zero matrix has rank 0.

What Is Matrix Rank?

The rank of a matrix is the number of linearly independent rows or columns. It is a key measure of how much information the matrix contains.

How to Calculate Matrix Rank

  1. Enter the matrix values.
  2. Use row reduction to find pivot positions.
  3. Count the number of pivot rows.
  4. That count is the matrix rank.
rank(A) = number of pivots

Worked Example

For [[1, 2, 3], [2, 4, 6], [1, 1, 1]], the rank is 2.

two pivot rows

Frequently Asked Questions

What does full rank mean?

A matrix is full rank when its rank equals the smaller of its row count and column count.

Can rank be zero?

Yes. The zero matrix has rank 0.

Can I enter decimals?

Yes. Any finite real matrix entries are accepted.

What if a cell is blank?

Blank cells are rejected instead of being silently converted to zero.

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