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).
Minors of a Matrix - dCode
Tag(s) : 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!
Minors of a Matrix
Minors of NxN Matrix Calculator
Answers to Questions (FAQ)
What is a matrix minor? (Definition)
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: $$ M = \begin{bmatrix} a & b & c \\ d & e & f \\ g & h & i \end{bmatrix} $$
The determinant of the sub-matrix obtained by removing the first row and the first column is: $ ei-fh $$, do the same for all combinations of rows and columns.
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 "Minors of a Matrix" source code. Any algorithm for the "Minors of a Matrix" algorithm, applet or snippet or script (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, breaker, translator), or any "Minors of a Matrix" functions (calculate, convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (Python, Java, PHP, C#, Javascript, Matlab, etc.) or any database download or API access for "Minors of a Matrix" or any other element are not public (except explicit open source licence like Creative Commons). Same with the download for offline use on PC, mobile, tablet, iPhone or Android app.
Reminder: dCode is an educational and teaching resource, accessible online for free and for everyone.
Cite dCode
The content of the page "Minors of a Matrix" and its results may be freely copied and reused, including for commercial purposes, provided that dCode.fr is cited as the source.
Exporting the results is free and can be done simply by clicking on the export icons ⤓ (.csv or .txt format) or ⧉ (copy and paste).
To cite dCode.fr on another website, use the link:
In a scientific article or book, the recommended bibliographic citation is: Minors of a Matrix on dCode.fr [online website], retrieved on 2025-04-16,
