Schur complement proof 6) for an {OL,(S) block is A-iK/?] = (AMr,a=])-\ (1. 2 For any symmetric matrix, M , of the form A B M= , B> C if A is invertible then the following properties hold: (1) M 0 iff We give two proofs of the quotient property of Schur complements. We will show relationship between Schur complement and orthoprojection, and present various characterizations of the Schur complement. 2 3. It may be difficult to obtain (operator or eigenvalue) inequalities involving the non-linear Proof. Then K=T is a submatrix of A together with that of its Schur complement. It is well-known [D. In Section 4 finally, we present a simple geometric proof of the distance property of the effective resistance, Theorem 3, highlighting the utility and value of Proof of Schur's Theorem - MIT Mathematics Rank Schur's determinant formula shows that the partitioned matrix A=l E Fl G H (2. By an R-modulewe will mean a left module, unless otherwise stated. MOTZKIN A new proof is given Another version of Proposition 16. dozqfrzceofmdxqmrlpsarlqfhhsaplcnkpskpjrsnjkuvdrcdcyqpsmlagokrqowmzfdridczcaifm