Orthogonal matrix whose submatrix has special properties

Thread starter julie94
Start date Oct 20, 2009
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Matrix Orthogonal Properties

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The discussion revolves around proving that the matrix A'A is idempotent when P is an n*n orthogonal matrix defined as P = (A B). The user expresses uncertainty on how to begin the proof and shares their initial steps, including the expression for PP' and its relation to the identity matrix In. The focus is on the properties of orthogonal matrices and the implications for the submatrix A. The thread seeks guidance on how to proceed with the proof.

Oct 20, 2009

julie94

Dear Forumers.

I am working on the following problem.

Let matrix P=( A B ) where A and B are matrices. Let P be an n*n orthogonal matrix.

Show that A'A is an idempotent matrix.

I do not know where to start. Thanks in advance for the help.

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Oct 20, 2009

julie94

I can write
PP'=(A B)(A B)'
=(AB'+AA' BB' +BA')

and I can write
PP'=In

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