This year started with heartbreak. The multiplication of all the eigenvalues is determinant of the matrix. (and the sum of all the eigenvalues is trace of the matrix. These properties are amazing!) I read an astonishing simple proof using diagonalization of a matrix. This blog is about that proof.
Matrix A can be diagonalize to
By the way,
A determinant is a scalar value, therefore, they are commutative. Therefore,
- Gilbert Strang, Introduction to Linear Algebra, Chapter 6.