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# ps4 - (i.e P is the matrix that projects R n onto range(A T...

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Problem Set #4 IE 417 Due November 5, 2002 1. a. A matrix P R n × n is called a projection matrix if P = P T and PP = P. Prove that if P is a projection matrix, then The matrix I -P is also a projection matrix, P is positive semi-definite, ||P x || || x || 2200 x R n . b. Show that if A R m × n , then P = A T (AA T ) -1 A is a projection matrix and that P x range(A T ) = {A T y : y R m } 2200 x R n
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Unformatted text preview: (i.e., P is the matrix that projects R n onto range(A T ). c. Show that I-P is also a projection matrix such that (I-P) x ∈ null(A) = { x ∈ R n : A x = 0} 2200 x ∈ R n (i.e., (I-P) is the matrix that projects R n onto null(A)). 2. 8.8 3. 8.22 (compare Hooke and Jeeves, Rosenbrock, steepest descent, and DFP) 4. 8.27 5. 8.40...
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