This expansion allows to compute the determinant a n n matrix by reducing it to a sum of determinants of (n 1) (n 1) matrices. It is still not suited to compute the determinant of a 20 20 matrix for example …

Determinants: definition, examples, and basic properties The linearity of determinants in one row or one column Computing determinants via elementary row and column operations

This fact, combined with the fact that the determinant of a matrix is also a multilinear alternating map of its columns is often useful for finding short-cuts in computing determinants.

Lots of useful formulas for 2 2 and 3 3 matrices can be expressed in terms of determinants, and determinants played a central role in linear algebra 100 years ago when most matrices were tiny. …

Now halfway through the course, we leave behind rectangular matrices and focus on square ones. Our next big topics are determinants and eigenvalues. The determinant is a number associated with any …

By applying the determinant operator to equation (50), and using the fact that the determinant of the matrix product is the product of the matrix determinants we see that V1 = jdet(L)j V0: (52) This …

We usually won't use the construction to actually compute determinants because there are much better ways. There are some special matrices where this construction gives a quick method of evaluation, …