Share Your Experience: Take the 2024 Developer Survey

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Accepted

### How do you find the homography matrix given 4 points in both images?

To understand homographies and how to find them, you will need a good dose of projective geometry. I will briefly describe some preliminary concepts that you need to know before trying to find the ...
• 40.8k
Accepted

### How to express a fully connected neural network succintly using linear algebra?

The equation $$\hat{y} = \sigma(xW_\color{green}{1})W_\color{blue}{2} \tag{1}\label{1}$$ is the equation of the forward pass of a single-hidden layer fully connected and feedforward neural network, i....
• 40.8k

### Is there any difference between affine transformation and linear transformation?

In linear algebra, a linear transformation (aka linear map or linear transform) $f: \mathcal{V} \rightarrow \mathcal{W}$ is a function that satisfies the following two conditions $f(u + v)=f(u)+f(v)$ ...
• 40.8k

• 40.8k
1 vote
Accepted

### What exactly is the eigenspace of a graph (in spectral clustering)?

In spectral clustering we not find the eigenvectors of a graph (a graph is not a matrix) but the eigenvalues/eigenvectors of the Laplacian matrix related to the adjacency matrix of the graph: graph =&...
• 1,293
1 vote

### What do we mean by 'principal angle between subspaces'?

Let's consider the case where you have two photos, one base photo and one other photo which is a scaled version of the base photo. Consider then that you could create a 'mapping' from the base photo ...
• 186
1 vote

### Is there any way to apply linear transformations on a vector other than matrix multiplication?

You can sometimes exploit the structure of your matrix to perform faster matrix multiplication. For example, if your matrix is sparse (or dense), there are algorithms that exploit this fact. In your ...
• 40.8k
1 vote

### Which linear algebra book should I read to understand vectorized operations?

Linear Algebra Done Right by Axler seems to be the best book on linear algebra, with a brisk and modern approach.
• 2,101
1 vote

### Using reinforcement learning to find a preconditioner for linear systems of the form Ax = b

Reinforcement Learning is a method for learning to perform beneficial actions in an environment. One way this is accomplished is by learning to predict useful actions as a function of the observed ...
• 9,267

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