# Questions tagged [linear-algebra]

A field of mathematics concerned with the study of finite dimensional vector spaces, including matrices and their manipulation, which are important in statistics.

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### SVD Kernel and Linear Algebra Kernel, is there a conceptual difference?

Is the term kernel used in Sklearn to execute the SVD machine learning algorithm conceptually related to the notion of a kernel in linear algebra ( null space )? Or do they happen to use this same ...
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### In Ax = b, why does x not pass through the origin? [migrated]

I am facing some difficulty in understanding the concept of x being a vector which doesn't pass through the origin. Let me tell you what I understand : A subspace is a space that contains all linear ...
52 views

### Removing constant from the regression model

I am trying to calibrate two variables $(X,Y)$ of different measuring techniques from two instruments, the result of the linear regression analysis appears as shown in the image. The result shows the ...
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### Understanding the algebra behind a specific partial derivative equation

I am following this article about neural networks. Given: Until here I understand everything, but then he continues to: I don't understand how he got to that conclusion. I think he skipped some ...
24 views

### 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 ...
75 views

### Dose finding slope/intercept using the formula of m,b gives best fit line always In linear regression?

In liner regression We have to fit different lines and chose one with minimum error so What is the motive of having a formula for m,b that can give slope and intercept value in the regression line ,...
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### Normal equation for linear regression is illogical

Currently I'm taking Andrew Ng's course. He gives a following formula to find solution for linear regression analytically: $θ = (X^T * X)^{-1} * X^T * у$ He doesn't explain it so I searched for it and ...
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### When is it useful to measure the Frobenius norm of a matrix?

In Deep Learning section 2.5 the author review some measures for the size of vectors and matrices. When in general is it useful for someone to know these? For instance they give the example of the ...
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### Predicting a variably-placed value in a vector

I have $m$ vectors in $\mathbb{R}^n$, where $m >> n$, and I want to train a model to impute a value $x_i$ in $\mathbf{x}$, where $1 \leq i \leq n$ (and can vary by vector). For instance, I may ...
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### Intuition behind understanding eigenvectors and Machine Learning

I am struggling to understand linear algebra application in machine learning, and I am not able to answer the following question. Is the model learned in Machine Learning the eigenvector of the ...
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### What are some theoretical approches to study Machine Learning/Deep Learning?

I've recently studied "basics of machine learning" (chapter 5) in Deep Learning by Ian Goodfellow. They're explaining ML with most of statistical and probabilitical methods. But I wish to ...
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### Projecting 3D Chemical Data Onto a 2D Plane in Motion

I'm trying to model the rotation of two hydrogen atoms about a carbon atom. Say I have a conceptual wheel on an axle that is attached to my car. The axle is described by two points in 3D space, as ...
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### How to calculate latent vector for a user in ALS based on some new input?

So I have an ALS trained in pyspark but then I get some interactions from a new user that wasn't in the training set. I want to give recommendations to that new user without retraining the ALS based ...
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### Can all known ML algorithms be written as a sequence of matrix operations?

I keep hearing that machine learning is just linear algebra. Does that mean all known (and all possible?) ML algos, from random forest, to support-vector machines, to recursive neural networks, can ...
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### How to solve Ax = b for A [closed]

Given two know vector x, and b (dimension 3*1 for example), what are the ways to approximate the matrix ...
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### Why transpose of independent feature matrix is necessary in case of linear regression?

I can follow classical linear regression steps: $Xw=y$ $X^{-1}Xw=X^{-1}y$ $Iw=X^{-1}y$ $w=X^{-1}y$ However, on implementing in Python, I see that instead of simply using ...
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### Linear regression with a fixed intercept and everything is in log

I have a set of values for a surface (in pixels) that becomes bigger over time (exponentially). The surface consists of cells that divide over time. After doing some modelling, I came up with the ...
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### Can we think of neurons as maps between matrices?

Usually when we think about neurons, we imagine that they enact some kind of map between real numbers. For example, a neuron might take in real numbers $x_{i}$ and weight them with parameters $W_{ij}$,...
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### Structures for incorporating linear functions into a nonlinear optimization problem

I'm working on a problem which naturally involves both linear and nonlinear operations, and I'd like some help understanding the best way to combine these into a neural network framework. To be more ...
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### Machine learning PhD Interview technical questions [closed]

I'm Software Engineer who applied to grad school for Machine Learning/Computer Vision PhD and currently waiting for interview calls. I'm brushing up Linear algebra/ ML topics. What kind of technical ...
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### How can I implement tangent distance for k-nearest neighbor in python/scikit-learn?

My ultimate aim is to have a function which I can feed into scikit-learn's NearestNeighbor class as a custom metric parameter. ...
63 views

### Linear algebra library for c++

I have been trying to find the substitute of numpy and perform some linear algebra using c++ and here's a list of libraries I have encountered: Eigen Armadillo Dlib GNU Scientific library Please ...
347 views

### Statistics Before Linear Algebra?

I know this is an opinion-based question and will be closed but this is the only place I know that can answer it reasonably and it is a very important matter to me. I am pursuing a machine ...