Solution Found!
(See the discussion on p. 167 and Exercise 3.4.25.) Let A be an n n matrix. Prove that
Chapter 4, Problem 24(choose chapter or problem)
QUESTION:
(See the discussion on p. 167 and Exercise 3.4.25.) Let A be an n n matrix. Prove that the functions A : R(A) C(A) and AT : C(A) R(A) are inverse functions if and only if A = QP, where P is a projection matrix and Q is orthogonal.
Questions & Answers
QUESTION:
(See the discussion on p. 167 and Exercise 3.4.25.) Let A be an n n matrix. Prove that the functions A : R(A) C(A) and AT : C(A) R(A) are inverse functions if and only if A = QP, where P is a projection matrix and Q is orthogonal.
ANSWER:Step 1 of 3
It is given that is matrix.
It is known that, is a one-one function.
Suppose and are inverse functions.
Then,