"Let me connect these special matrices A and S to calculus. The vector x changes to a function x(t). The differences Ax become the derivative dx/ dt = bet). In the inverse direction, the sum Sb becomes the integral of bet)."
"When E multiplies on the right, it acts on the columns of A."
"Schur complement."
"To solve A x = b without A-I, we deal with one column b to find one column x."
"Suppose there is a nonzero vector x such that Ax = 0"
"A triangular matrix is invertible if and only if no diagonal entries are zero."
"The column space C (U) consists of all vectors of the form (b I , b2 , b3 , 0)."