On Saturday, March 19, 2016 at 4:31:04 AM UTC+1, Travis Scrimshaw wrote: > > Hey all, > We ended up needing to compute the determinant of a 0x0 matrix in > #17030.Sage currently says the following: > > sage: mat = matrix(ZZ, 0, 0) > sage: mat.det() > 1 > > However, the code (and myself) was expecting this to be 0 as the sum in the > definition is vacuous. > > Although, in a sense, the 0x0 matrix is its own inverse, so this might be an > argument for having it be 1. > > Thoughts? > > Using the Leibniz formula as the definition, the determinant of an n by n matrix is a sum of products, one product for each of the n! permutations on n elements. When n = 0, there is exactly one such permutation, the identity permutation of the empty set, so there is one term in the sum for the determinant, and its value is 1 since it is the empty product.
This convention also agrees with the determinant being the product of all eigenvalues, and other useful properties. Fredrik -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at https://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
