Solved: Suppose the block matrix A on the left side of (7)
Chapter 2, Problem 17E(choose chapter or problem)
Problem 17E
Suppose the block matrix A on the left side of (7) is invertible and A11 is invertible. Show that the Schur complement S of A11 is invertible. [Hint: The outside factors on the right side of (7) are always invertible. Verify this.] When A and A11 are both invertible, (7) leads to a formula for A–1, using S–1, , and the other entries in A.
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