let A be an m x n matrix...prove that N(A^T*A)=N(A) problem gives a hint vector x is a member of N(A^T*A) then A*vector x is a member of C(A) n N(A^T) B) prove that rank (A)=rank(A^T*A) C) prove that C(A^T*A)=C(A^T) Thanks
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Originally Posted by bugal402 let A be an m x n matrix...prove that N(A^T*A)=N(A) problem gives a hint vector x is a member of N(A^T*A) then A*vector x is a member of C(A) n N(A^T) B) prove that rank (A)=rank(A^T*A) C) prove that C(A^T*A)=C(A^T) Thanks What is N(A), C(A)...?? Tonio
n(a) is null space c(a) is column space sorry about that
Originally Posted by bugal402 let A be an m x n matrix...prove that N(A^T*A)=N(A) problem gives a hint vector x is a member of N(A^T*A) then A*vector x is a member of C(A) n N(A^T) B) prove that rank (A)=rank(A^T*A) C) prove that C(A^T*A)=C(A^T) If then obviously . Therefore . For the converse, suppose that . Then , which implies that . For B), use the rank+nullity theorem.
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