Suppose A is a real m x n matrix. a) Prove that the symmetric matrix AT...

 

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Suppose A is a real m x n matrix. a) Prove that the symmetric matrix AT A has the property x² (ATA)x ≥ 0 for every vector x in Rn. [5 pts] b) According to part a), the matrix AT A is positive semidefinite at least and possibly positive definite. Under what condition A on is AT A positive definite? [5 pts] Suppose A is a real m x n matrix. a) Prove that the symmetric matrix AT A has the property x² (ATA)x ≥ 0 for every vector x in Rn. [5 pts] b) According to part a), the matrix AT A is positive semidefinite at least and possibly positive definite. Under what condition A on is AT A positive definite? [5 pts]