# Questions tagged [vectorization]

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

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### Derivative of determinate function w.r.t. matrix with vectors

For my research, I need to calculate a derivative of scalar determinate function w.r.t. matrix with vectors Here is a scalar defined as $c = \sqrt{det(A)}$ $\mathbf{A}=\mathbf{JJ}^T$ where $\mathbf{J}$...
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### Vectorizing a matrix that is not full column rank

Let $A\in\mathbb{R}^{n\times m}$ be a matrix that is not full column-rank $\text{rank}(A) = k$ for some $k < m$. Now I vectorize this matrix $$a = \text{vec}(A) \in\mathbb{R}^{nm\times 1}.$$ Is ...
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### On the relation between the vectorization and the half vectorization

From Matrix Variate Distributions by Gupta & Nagar. 1) definition of vectorization for a generic matrix (page 9) Let $X$ be a $m\times n$ matrix and let $X_1$, $\dots$, $X_n$ be the columns of $X$ ...
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### Derivative of Vectorization of matrix products w.r.t. a matrix

Suppose $\lambda \in l\times1$， $y \in l\times 1$，$A \in l\times mn$， $L \in m\times r$，$R \in n\times r$ $f=1/2 \parallel L\parallel_{F}^{2} + \lambda^{T} (y-A \text{vec}(LR^{T}) )$ I want to ...
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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)
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### weighted median, but manually typed weights, not frequencies

Since theres some contoversy about the definition of the weighted median, I wonder if my doing is even possible: I have a large 2d matrix ...
1 vote
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### About standard vectorization of a matrix and its derivative

I read about this notation: if $X \in \mathbb{R}^{d\times d}$ then $X^b \in \mathbb{R}^{d^2}$ is the standard vectorization of $X$. I searched the term "standard vectorization" and only ...
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### How to do vectorization for summation for octave implementation?

I am trying to understand the transformation from a summation form to vectorization (or a form of matrix multiplications) in order to implement it in some programming language (octave or python or ...
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### Is a square commutation matrix positive semidefinite?

Let $A \in \mathbb{R}^{n \times n}$ and denote the commutation matrix, made up of 0 and 1 such that each row and each column has exactly one 1, as $K_{n} \in \mathbb{R}^{n^2 \times n^2}$ , which is ...
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### Can I write this sum as a matrix product?

Let $\eta$ be a $n \times p$ matrix and $\Sigma$ a $p\times p$ matrix. Is it possible to rewrite the sum over element-wise quadratic forms, $$\sum_{i=1}^n \eta_i^T \ \Sigma \ \eta_i,$$ where $\eta_i$...
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### Find $\frac{dY}{dX}, Y=(X')^{2}B$ matrix derivative

I have the following problem: Find the matrix derivative $\frac{dY}{dX}$, where $Y=(X')^2B$, matrix $X$ is $p \times q$ and $B$ is a given matrix. I have gotten this far: By matrix derivative ...
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### Kronecker products: Reordering $\text{vec}(A) \text{vec}(A)^T$ to $A \otimes A$

I'm trying to find a more elegant way to reorder the elements of the Kronecker product $\text{vec}(\textbf{A})\text{vec}(\textbf{A})^T$ into those of $\textbf{A} \otimes \textbf{A}$, where $\textbf{A}$...
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### Permuting tensor indices and relations to rearranging factors in a general-size kronecker product operators on same space?

Given the following conjecture, we can start considering larger than $2$ factor Kronecker products. Let us say we define: $$R_1\otimes R_2 \otimes \cdots \otimes R_N$$ And then the operation "...
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### Derivative of vectorized block matrix in terms of derivatives of vectorized blocks

Suppose I have some block matrix $\pmb{Y}$ that is a function of $\pmb{x}$: $$\pmb{Y} = \begin{bmatrix} \pmb{A} & \pmb{C} & \pmb{E} \\ \pmb{B} & \pmb{D} & \pmb{F} \\ \end{bmatrix}.$$ ...
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### Derivative of matrix w.r.t. its own vectorized version

I am unable to find what would be the derivative of a $m \times m$ real matrix $A$ with respect to $(\mathrm{vec}(A))^T$ (where $T$ is transpose and $\mathrm{vec}$ stacks the columns) without using ...
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### Cost function - vectorized implementation

I have a problem regarding how to vectorize, more specifically the problem below: Repeat { $$\theta_j := \theta_j - \frac{\alpha}{m} \sum\limits_{i=1}^m (h_\theta(x^{(i)}) - y^{(i)})x_j^{(i)}$$ } ...
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### Solve vectorial equations

I'm trying to figure out a passage for reducing a vectorial equations ! for doing this somebody told me to use a program of symbolic calculation (matlab,maple, mathematical .. or python as well .. ) I ...
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### Vectorization of expressions: How to develop a visual intution

I'm currently analyzing the expressions for backpropagation in machine learning and it takes me a lot of time to convert my derived formulas into matrices. I can't find anything helpful on google, ...
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### Finding Hessian of tr ((AB)' (AB))

I'm trying to find Hessian of $\text{tr}((AB)' (AB))$ where $A,B$ are matrices. There are nice expressions for $H_{AA}$ and $H_{BB}$ using standard approach from Magnus 1 , can anyone suggest how to ...
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I have a diabatic potential energy matrix, $V(r,Z)$, (real symmetric) for a 2-level system with two nuclear coordinates, $(r,Z)$:  V(r,Z)= \begin{pmatrix} V_{11}(r,Z) & V_{12}(r,Z)\\ V_{12}(r,...