I have matrix $A = \begin{bmatrix}1 & -4 & 3\end{bmatrix}$. Is there a matrix that this can be multiplied by (or any other operations) to produce a matrix like this: $\begin{bmatrix}1&-4&3&0&0&0\\0&1&-4&3&0&0\\0&0&1&-4&3&0\\0&0&0&1&-4&3\\\end{bmatrix}$? I was thinking it might be something similar to an identity matrix but I was not sure how to find it. Thanks!
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No for multiplication, because the matrix size won't match. – Wojowu Sep 26 '15 at 08:16
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Looks like convolution with a $4\times4$ identity matrix to me. – peterwhy Sep 26 '15 at 08:44
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Your resultant matrix is equal to the result of the following convolution: $$\begin{bmatrix}1&-4&3\end{bmatrix}* \begin{bmatrix} 1&0&0&0\\ 0&1&0&0\\ 0&0&1&0\\ 0&0&0&1 \end{bmatrix} = A*I_4,$$ with the treatment that convolution of two matrices may enlarge matrix size, instead of wrapping or trimming the resultant matrix.
peterwhy
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