About QR decomposition

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While studying matrix QR decomposition I've found the following:

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I understand the general idea. But, in the Proof, $A = (a_1, ..., a_n)$. What are $a_1, ..., a_n$? They are elements of matrix $A$? Why they are not written as $a_{ij}, ...$?

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They are the column vectors of the matrix $A$.