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*!

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 $).

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.

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.

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, breaker, 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, mobile, tablet, iPhone or Android app!

Reminder : dCode is free to use.

The copy-paste of the page "Minors of a Matrix" or any of its results, is allowed (even for commercial purposes) as long as you credit dCode!

Exporting results as a .csv or .txt file is free by clicking on the *export* icon

Cite as source (bibliography):

*Minors of a Matrix* on dCode.fr [online website], retrieved on 2024-11-11,

minor,matrix,determinant,square

https://www.dcode.fr/matrix-minors

© 2024 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaching / CTF.

Feedback