Some functions allow you to specify the method (algorithm) to be used to carry out the function. For example, the Determinant function lets you choose from many methods, including 'float', 'minor', and 'rational'. If you know your Matrix has particular characteristics, you can specify an appropriate algorithm, making the computation faster.
M is an upper triangular Matrix, and this information is readily available to the Determinant function.
>
|
|
N is also an upper triangular Matrix, but this information is not readily available to the Determinant function because its shape is 'rectangular'.
The Determinant function uses the fact that M is upper triangular to select an appropriate algorithm and returns an answer in a negligible amount of time:
>
|
|
With no information about , the Determinant function does not necessarily make the most efficient algorithm choice, and takes longer:
>
|
|
When the user specifies the method, the Determinant function can work as quickly on N as it did on M. (The minor expansion is done along the first column, and since the first column of an upper triangular Matrix is mostly zeros, the computation is very fast for upper triangular Matrices.)
>
|
|
For more information, see the Determinant help page.