I have a vector that I sliced into k vectors to create a matrix that is kxn. Let's call this matrix A (kxn) when I multiply the transpose of A (nxk) with A(kxn) I get a square matrix B(nxn) what does B signify?
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Please try to be more clear. Are you slicing into $k$ vectors all with the same size? And what is $k$? Any divisor of $n$? Finally, the question itself might be seen as going against this part of the FAQ: What kind of questions should I not ask here? – Git Gud Mar 23 '13 at 15:40
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I am slicing into k vectors all the same size (n). All I'm simply asking is: if I have a matrix A(kxn) and I multiply it as follows A^T*A, what do I get? Is it an autocorrelation? A covariance variance matrix? – user68147 Mar 23 '13 at 15:47
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If $A$ is a matrix made of column vectors $v_1,\dots,v_k$, then $A^TA$ is the Gramian matrix (but it has size $k\times k$, not $n\times n$).
If the vectors are centered random variables, the Gramian is proportional to the covariance matrix
The $n\times n$ matrix would be $AA^T$. This is the sum of outer products $v_i\times v_j$ over all $i$ and $j$; but it's probably better understood as the Gramian matrix of the rows of $A$.
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