Matrix Rank Calculator

Find the rank of a 2x2, 3x3, or 4x4 matrix by reducing to row echelon form and counting pivots. The rank tells you how many linearly independent rows or columns it has.

Frequently Asked Questions

What is matrix rank?

The maximum number of linearly independent rows or columns. Equivalently, the dimension of the image of the linear map defined by the matrix.

Rank versus determinant?

For a square matrix, full rank is equivalent to a nonzero determinant. Rank generalizes to non-square matrices and is more numerically stable to compute via row reduction or SVD.

What is rank-nullity?

For an m by n matrix, rank + nullity = n where nullity is the dimension of the null space (vectors x with A times x equal to zero). It is the fundamental relation between image and kernel dimensions.

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Estimates for informational purposes only.

Important Disclaimer: Estimates for informational purposes only.

This calculator provides estimates for informational purposes only. Results are based on assumptions and may not reflect actual outcomes. Consult qualified professionals in relevant fields before making important decisions based on these results.

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