homechevron_rightStudychevron_rightMathchevron_rightAlgebrachevron_rightlinear algebra

Determinant of a matrix

This online calculator computes determinant of a matrix, using it's definition

The site engine now allows input of long texts, so this is first calculator to use this feature, and it is used to enter matrix, and calculator computes the determinant of entered matrix.

It uses determinant definition, which is recursive calculation, and, in theory, quite resource consuming, but for our case, with matrix, entered manually, I believe it is enough (if not, please use Determinant by Gaussian elimination).

Some notes about determinant are below the calculator, for those who forgot.

PLANETCALC, Determinant of a matrix

Determinant of a matrix

Digits after the decimal point: 2
Determinant of a matrix

Some recursive formulae:

det A=\begin{vmatrix} a_{11}\end{vmatrix} = a_{11}

  • determinant of a matrix 1x1

det A=\begin{vmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{vmatrix}=a_{11}a_{22}-a_{12}a_{21}

  • determinant of a matrix 2x2

det A=\sum_{j=1}^n (-1)^{1+j} a_{1j}\bar M_j^1

  • determinant of a matrix nxn, where n > 2
    \bar M_j^1 - minor of a_{1j}.
    Minor of a_{1j} - is the determinant of a (n–1) × (n–1) matrix that results from deleting the 1-th row and the j-th column of A. That's why this is recursive definition.

For example, here is the determinant of a matrix 3x3
det A =  \begin{vmatrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \end{vmatrix} = a_{11}\begin{vmatrix}    a_{22} & a_{23} \\  a_{32} & a_{33} \end{vmatrix}-a_{12}\begin{vmatrix}    a_{21} & a_{23} \\  a_{31} & a_{33} \end{vmatrix}+a_{13}\begin{vmatrix}    a_{21} & a_{22} \\  a_{31} & a_{32} \end{vmatrix}

URL copied to clipboard
Creative Commons Attribution/Share-Alike License 3.0 (Unported) PLANETCALC, Determinant of a matrix