# Questions tagged [vector]

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### What is the derivative of a matrix with regard to a vector defined?

I had this question when I read equation (C.20) in Appendix C of "Pattern Recognition and Machine Learning" written by Christopher M. Bishop. Here I copy the equation below for reference: ...
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### How to define distance for vector of angles?

I have a vector of angles and I am looking for a method to compute the distance of my vector with any other vector of angles? I am looking for something similar to Euclidean distance but I know that ...
• 151
42 views

### Removing duplicate training vectors?

As an extension to this question, for ML problems where it makes sense to remove duplicates (ie: identical data & target variables) from your distribution, in which scenarios would it (if at all) ...
• 101
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### What is the difference between the dot product and the element-by-element multiplication?

What is the different between the dot product "$\cdot$" and the element-by-element multiplication notation $\odot$ in Statistics? I referred to Hamilton's Time-Series Analysis, and these ...
• 1,030
1 vote
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### rank of an expected value of a matrix

x is (a * 1) vector y is (b * 1) vector x and y are independent then what is rank(E[xy']) I know that xy' should be (a*b) matrix and since they are independent. , however I am not sure about the rank
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1 vote
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### Expected value of a product of two dependent random variables

Let me preface this by saying that I'm an engineer, and by no means a mathematician, so please excuse any mathematical "wrong-doing" in my explanation. I have two vectors $V_1$ and $V_2$, ...
• 11
87 views

### Length of a probability vector?

I'm doing some work on probability vectors, and came across the idea of probability vector length as a measure of how deterministic a probability vector is, as calculated using this equation: The ...
33 views

### How do I take the derivative to $\gamma$ of $(y-x^{\gamma})^T(y-x^{\gamma})$?

I have to solve the least squares for $\gamma$ in the following problem. The model is described as $y_i = \beta x_i^{\gamma} + u_i$, where $u_i$ is i.i.d. normal with mean zero and variance $\sigma^2$...
361 views

### Matrix and vectors, why different notation for dimensions?

If we collect data and put it into a matrix of size (100,3), we tend to say we have three-dimensional data. We think of each column as a dimension. On the other side, if we have a vector of size (100,...
• 241
1 vote
33 views

### What is the entropy of multivariate data multiplied by a vector?

It is a general rule that for multivariate data $\boldsymbol{X}$ and a matrix $\boldsymbol{A}$, their entropy is $$h(\boldsymbol{A} \boldsymbol{X}) = h(\boldsymbol{X}) + \ln |\det \boldsymbol{A}|$$ (...
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I have a little question, but I don't know that well how to answer it. I have a random walker with position vector $\vec{r} = \sum_{i=1}^N \vec{r}_i$, where i is the random walker's step. Every vector ...