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A matrix (plural matrices) is a rectangular array of numbers, symbols, or expressions arranged in rows and columns. The individual items in a matrix are called its elements or entries.

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Show that ABA=0 if and only if B is of the form C-PCP for some symmetric matrix C

If B is a symmetric matrix such that ABA is well-defined, then show that ABA=0 if and only if B is of the form C-PACPA for some symmetric matrix C. PA here is the projection matrix of A. …
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