Determinants, Triangular Matrices
Triangular Matrices
A lower triangular matrix has zeros above the main diagonal.
Use det2 to compute the determinant.
If row 1 selects anything other than column 1, the entry is 0,
and that permutation product is 0.
Now column 1 is used, and can't be used again.
If row 2 selects anything other than column 2, the entry is 0.
This continues all the way down to the last row.
The only nonzero term is the product of the main diagonal.
The same holds for an upper triangular matrix.
Call this formula det5.
It is restricted to triangular matrices,
but it is very valuable, as we shall see.