dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles and problems to solve every day! A suggestion ? a feedback ? a bug ? an idea ? Write to dCode!

Tool to calculate the rank of a Matrix. In mathematics, The rank of a matrix M is the number of linearly independent rows or columns.

Answers to Questions

What is the matrix rank? (Definition)

The rank of a matrix (sometimes noted as Rk) is mainly defined as the maximum number of row vectors (or column vectors) which are linearly independent.

The rank of a matrix is also the dimension of the vector subspace created by the vectors (either rows or columns) of the matrix.

The rank can be calculated for both rows and columns, it will be the same value.

How to calculate a matrix rank?

To calculate the rank of a $ M $ matrix, compare each of the rows between them and each of the columns between them to verify that they are two-by-two linearly independent.

Example: $$ M = \begin{bmatrix} 1 & 2 & 3 \\ 2 & 4 & 6 \\ 2 & 2 & 4 \end{bmatrix} $$ The matrix $ M $ has rank $ 2 $ because line 2 is twice the line 1, they are not linearly independent. NB: column 3 is the sum of columns 1 and 2, they are not linearly independent.

Source code

dCode retains ownership of the online 'Rank of a Matrix' tool source code. Except explicit open source licence (indicated CC / Creative Commons / free), any algorithm, applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (PHP, Java, C#, Python, Javascript, Matlab, etc.) no data, script or API access will be for free, same for Rank of a Matrix download for offline use on PC, tablet, iPhone or Android !

Need Help ?

Please, check our community Discord for help requests!