Matrix Rank
The rank of a matrix is the number of linearly independent rows — equivalently, the number of pivots in its row echelon form. Enter the matrix and the calculator row-reduces it and reports the rank.
Frequently asked questions
Is row rank the same as column rank?
Yes. For every matrix the number of linearly independent rows equals the number of linearly independent columns — this common value is the rank.
What does full rank mean?
An m×n matrix has full rank when its rank equals min(m, n). A square matrix has full rank exactly when it is invertible.
How does row reduction reveal the rank?
After reducing to row echelon form, each leading 1 corresponds to one independent row. The number of non-zero rows is the rank.