Рет қаралды 7,293
We explore the idea of taking a polynomial multiplied by an identity matrix, and factorising it into two matrices.
Further reading:
Crisler, D., & Diveris, K. (2016). Matrix factorizations of sums of squares polynomials. Pi Mu Epsilon Journal, 14(5), 301-306.
Eisenbud, D. (1980). Homological algebra on a complete intersection, with an application to group representations. Transactions of the American Mathematical Society, 260(1), 35-64.
00:00 Intro
01:07 2x2 Matrices
03:42 Polynomials with 2 terms
05:25 Polynomials with 3 terms
09:24 Block matrix multiplication
12:23 A possible 4x4 factorisation
16:06 Ensuring commutativity
18:36 Factorisation for 3 terms
20:00 Generalisation for 3 terms
22:21 Even more terms