Calculate the rank of a matrix (number of linearly independent rows/columns).
Matrix Configuration
Rank Analysis
2
Matrix Rank
Dimension of the vector space generated by the matrix columns/rows.
Nullity1
Full Rank?No
About this calculator
Quick Reference
Rank ≤ min(m, n)True
Rank(0)0
What is Matrix Rank?
The rank of a matrix is the maximum number of linearly independent row vectors or column vectors in the matrix. It represents the dimension of the image of the linear transformation determined by the matrix.
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Pro Tips
Row Rank equals Column Rank.
A square matrix is invertible if and only if its rank equals its size (Full Rank).
Rank + Nullity = Number of Columns (Rank-Nullity Theorem).
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Fun Facts
"The rank is one of the most fundamental properties of a matrix."
"If the determinant of an n×n matrix is non-zero, its rank is n."
