Search for a tool
Minors of a Matrix

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).

Results

Minors of a Matrix -

Tag(s) : Matrix

Share
dCode and more

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!

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

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

# Minors of a Matrix

## Minors of NxN Matrix Calculator

### 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. Except explicit open source licence (indicated Creative Commons / free), the "Minors of a Matrix" algorithm, the applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or the "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.) and all data download, script, or API access for "Minors of a Matrix" are not public, same for offline use on PC, tablet, iPhone or Android !
The copy-paste of the page "Minors of a Matrix" or any of its results, is allowed as long as you cite the online source https://www.dcode.fr/matrix-minors
Reminder : dCode is free to use.

## Need Help ?

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