Planned maintenance impacting Stack Overflow and all Stack Exchange sites is scheduled for Monday, September 16, 2024, 5:00 PM-10:00 PM EDT (Monday, September 16, 21:00 UTC- Tuesday, September 17, 2:00 UTC). The email/password authentication method will be unavailable for logging in and registering. Read more here

# Questions tagged [matrix]

A matrix (plural matrices) is a rectangular array of numbers, symbols, or expressions arranged in rows and columns. The individual items in a matrix are called its elements or entries.

935 questions
Filter by
Sorted by
Tagged with
62 views

### Comparing linear slopes between two scatterplot matrices

Below is a reproducible example of code that produces a dataset and plot roughly similar to what I am working on. The dataset is comprised of multiple columns for gene transcript abundance values and ...
• 1
13 views

• 121
60 views

### Sum of powers (geometric series) of state transition matrix

I am working discrete time Markov chain analysis for some large state transition graph. I want to find the rewards/cost to reach from the init state to the terminal/accepting states. I have the state ...
• 101
1 vote
33 views

### Derivative of structure matrices

I'm trying to follow 'Advanced Multivariate Statistics with Matrices', chapter 1.4. I know that this book is quite old, however I'm rather constrained with time and the papers I'm reading references ...
18 views

### Proof that regression coefficients are identical for averages over treatments data and raw data [duplicate]

The topic is somewhat related to this question. Let's say Experiment with treatments T0, T1, T2 with four repetitions for each and a response $y = (y_{0, 1}, y_{0, 2}, ..., y_{2, 4})$, one ...
• 111
75 views

### Frobenius norm of rank-constrained matrix product is bounded

Say I have three matrices $\mathbf{W} \in \mathbb{R}^{p \times m}$ and $\mathbf{A}, \mathbf{B} \in \mathbb{R}^{m \times n}$ with $\operatorname{rank}(\mathbf{A}) \leq r$ and $\mathbf{B}$ is ...
• 125
12 views

### How to convert pairwise dissimilarity matrix into continues predictor in R

I have collected plant species data and AGB from 25 different sites and I want to do regression analysis of Beta-diversity (i.e. dissimilarity among 25 sites) as a predictor and AGB as response ...
1 vote
76 views

### Noise Removal for Consistent Anomaly Detection in Multi-Dimensional Time Series Using Matrix Profile

In an online anomaly detection task involving multiple time series, I compute the left matrix profile using non-normalized Euclidean distances for each of the time series (Figure 1). However, since ...
• 183
1 vote
43 views

• 99
25 views

### Proving how scaling of predictor variable in linear regression, affects the fitted coefficient [duplicate]

In linear regression the OLS solution is given by: $$\hat{\beta} = (X^TX)^{-1}X^TY$$ I want to show that if you scale the $i$th predictor variable by a constant, then the corresponding $i$th ...
• 359
78 views

### In a linear model, why do we have $-2X^T \vec{y} + 2X^T X \vec{\beta}=0$? [duplicate]

When we derive the estimates of $\vec{\beta}$ such that they minimize the sum of squared error ($SSE$) we begin with $\sum_{i=1}^{n} (y_i - (\beta_0 + \beta_1x_1 + ... + \beta_kx_k))^2$. This is ...
1 vote
68 views

### How can we think about linear regression geometrically?

The simple linear regression model is given by $y_i = \beta_0 + \beta_1x_1 + e$ It is my understanding that it can be rewritten in matrix vector form as $\vec{y} = X\vec{\beta} + \vec{e}$ where $X$ is ...
71 views

### Similarity and Prevalence in Binary Vectors

Let's say I have N vectors, all of length L. Each vector is binary, such that they comprise of 0s and 1s whereby a 0 represents an 'absence' and 1 represents a 'presence' of an element denoted by its ...
• 29
50 views

### How do we prove that the rows or columns of a hat matrix sum up to 1, when mean function includes an intercept? [duplicate]

Every textbook I encounter tells me that this is simply a meaningful relationship of a hat matrix, without explaining why: If H is the hat (projection) matrix, and our X matrix has full rank and a ...
34 views

### Calculate multivariate betas using correlations and standard deviations [duplicate]

In a simple regression context: $$y = \alpha + \beta x + e$$ We can estimate beta from: $$\hat{\beta} = \frac{cov(x,y)}{var(x)} = \rho_{xy} \frac{\sigma_y}{\sigma_x}$$ This last decomposition is ...
125 views

### multicollinearity and categorical variables

When performing regression with categorical variables, in order to avoid multicollinearity, it is necessary to drop one level. This is clear in fact: Let's assume I have a binary categorical variable (...