Matrix Determinant

Given a matrix, , its determinant can be written as or .

A determinant can only be calculated from a square matrix.

The determinant of a matrix:

The determinant of a matrix:

The determinant of a matrix:

More generally, to calculate the determinant of a matrix, for example:

Take the first row:

Make every second element negative:

For each element, ignore the row and column it's in:

And multiply it by the determinant of the remaining elements:

Then recursively decompose the resulting determinants until you're left with the trivial case of a single-element matrix.

(the above method applies to and matrices, but it helps to have a bigger matrix for demonstration)

Determinants have the property that: