Tool for calculating the minors of a matrix, i.e. the values of the determinants of its square sub-matrices (removing one row and one column of the starting matrix).

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!

The minors of a square matrix $ M = m_{i, j} $ of size $ n $ are the determinants of the square sub-matrices obtained by removing the row $ i $ and the column $ j $ from $ M $.

Sometimes minors are defined by removing opposing rows and columns (ie. row $ n-i $ and column $ n-j $).

How to calculate a matrix minors?

For a square matrix of order 2, finding the minors is calculating the matrix of cofactors without the coefficients.

For larger matrices like 3x3, calculate the determinants of each sub-matrix.

Example: $$ M = \begin{bmatrix} a & b & c \\ d & e & f \\ g & h & i \end{bmatrix} $$

What is the difference between a minor and a cofactor?

For a square matrix, the minor is identical to the cofactor except for the sign (indeed, the cofactors can have a - sign depending on their position in the matrix). Minors do not take this minus sign.

Source code

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

Need Help ?

Please, check our dCode Discord community for help requests! NB: for encrypted messages, test our automatic cipher identifier!

Questions / Comments

Thanks to your feedback and relevant comments, dCode has developed the best 'Minors of a Matrix' tool, so feel free to write! Thank you!

Thanks to your feedback and relevant comments, dCode has developed the best 'Minors of a Matrix' tool, so feel free to write! Thank you!