# Questions tagged [linear-algebra]

For questions about the use/aspects/implementation/intuition/mathematical proofs of various Linear Algebra methods used in Machine Learning and AI algorithms.

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### What does it mean to do multi-dimensional processing with tensors in tensor cores?

In some tweets about NeurIPS 2018, this video from NVIDIA appeared. At around 0.37, she says: If you think about the current computations in our deep learning systems, they are all based on Linear ...
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### How to express a fully connected neural network succintly using linear algebra?

I'm currently reading the paper Federated Learning with Matched Averaging (2020), where the authors claim: A basic fully connected (FC) NN can be formulated as: $\hat{y} = \sigma(xW_1)W_2$ [...] ...
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### Which linear algebra book should I read to understand vectorized operations?

I am reading Goodfellow's book about neural networks, but I am stuck in the mathematical calculus of the back-propagation algorithm. I understood the principle, and some Youtube videos explaining this ...
425 views

### How does neural network classifier classify from just drawing a decision plane?

I understand that a neural network basically distorts(non-linear transformation) and changes the perspective(linear transformations) of input space to draw a plane to classify data. How does the ...
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### Why MLP cannot approximate a closed shape function?

[TL;DR] I generated two classes Red and Blue on a 2D space. Red are points on Unit Circle and Blue are points on a Circle Ring with radius limits (3,4). I tried to train a Multi Layer Perceptron ...
77 views

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

Consider the following statements from A Simple Custom Module of PyTorch's documentation To get started, let’s look at a simpler, custom version of PyTorch’s Linear module. This module applies an ...
193 views

### How can we find the value function by solving a system of linear equations?

I am following the book "Reinforcement Learning: An Introduction" by Richard Sutton and Andrew Barto, and they give an example of a problem for which the value function can be computed ...
761 views

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

I want to understand the process of finding a homography matrix given 4 points in both images. I am able to do that in python OpenCV, but I wonder how it works behind the scenes. Suppose I have ...
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### How to find distance between 2 points when dimensions are all of different nature?

I have a dataset with four features: the x coordinate the y coordinate the velocity magnitude angle Now, I want to measure the distance between two points in the dataset, taking into account the ...
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### Human intuition behind SVD in case of recommendation system

This does not answer my question. I struggled very hard to understand the SVD from a linear-algebra point of view. But in some cases I failed to connect the dots. So, I started to see all the ...
92 views

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

I came across the term 'principal angle between subspaces' as a tool for comparing objects in images. All material that I found on the internet seems to deal with this idea in a highly mathematical ...
44 views

### Simplifying Log Loss

I am reading through a paper (https://www.mitpressjournals.org/doi/pdf/10.1162/0891201053630273) where they describe logloss as a ranking function and can be simplified to the margin of the training ...