Mathematics Stack Exchange
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Questions tagged [vectorization]

The vectorization of a matrix is a linear transformation that converts the matrix into a column vector.

The vectorization of an $m \times n$ matrix $A$, denoted by $\mbox{vec} (A)$, is the $m n \times 1$ column vector obtained by stacking the columns of matrix $A$ on top of one another.

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How to "de-vectorise" a matrix? Is first column at the bottom or at the top?

I need to transform a 15x1 matrix into a 3x5 one. Is the first 3x1 column at the top, as Wikipedia seems to suggest? https://en.wikipedia.org/wiki/Vectorization_(mathematics)
Svit
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Any body knows the name of the product $A\circ B$, It is not Hadamard tensor product

I have seen this operation in a vectorization operation of $D=AX^{T}B$ i.e. $vec(D)=\left( A\circ B\right) vec(X),$ \begin{equation*} A\circ B= \begin{pmatrix} A_{1}B_{1}^{T} & A_{2}B_{1}^{T} & \cdots & A_{n}B_{1}^{T} \\ A_{1}B_{2}^{T} &…
core
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Vectorization identity proof

I'm trying to prove the identity $\vert vec(AXB)\rangle = A\otimes B^T \vert vec(X)\rangle$, where $\vert vec(L)\rangle := \sum_{ij} L_{ij}\vert i\rangle\vert j\rangle$ for any $L:= \sum_{ij}L_{ij}\vert i\rangle\langle j\vert$. The left hand side…
user1936752
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