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# Determinant mathematics

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Determinants only make sense when dealing with square matrices.

The determinant of a one by one matrix is simply the number itself (necessary to mention for thoroughness).

The determinant of a two by two matrix

a1,1 | a1,2
a2,1 | a2,2

is: a1,1 * a2,2 - a2,1 * a1,2

To do a larger matrix do as follows:

1. pick a row or column (preferably one with a lot of zeros in it since it will make your job easier),
2. write an element from the row or column you've chosen,
3. if the indices (in the example above, the sub script numbers are the indices) add up to an odd number, change the sign of the element you wrote down,
4. multiply this number by the determinant of the matrix of all the numbers that are not in the same row or column as the element you wrote down (you should have a square matrix that is smaller by one row and one column than the original),
5. repeat from step 2 for all the elements in the row or column you chose,
6. add all the terms up.

The recursive definition can be a pain, but if you take your time and watch for mistakes you'll be fine.

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Last edited August 16, 2001 12:11 am (diff)
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