How to Prove Rank(A) Equals Rank(ATA)?

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Thread starter katyyara
Start date Jan 30, 2010
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Matrix rank

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katyyara

Thread starter
Jan 30, 2010

Hi,

Does anyone know how to prove rank(A)=rank(AT A) where A is any matrix and AT is the transposed of matrix A? I have difficulty to prove the part that nulity(A)=nulity(AT A). Any help will be appreciated.

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rochfor1

Jan 30, 2010

Try proving [tex]\operatorname{ker} A = \operatorname{ker} ( A^\top A)[/tex].

How to Prove Rank(A) Equals Rank(ATA)?

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