# 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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### How does tensor product/multiplication work in TensorFlow?

In Tensorflow, I saw the following example: ...
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### Finding linear transformation under which distance matrices are similar

I have $n$ sets of vectors, where each set $S_i$ contains $k$ vectors in $\mathbb{R}^d$. I know there is some unknown linear transformation $W$ under which the distance matrix $D_i$ (a $k\times k$ ...
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### What is the use of additional column of 1s in normal equation?

Currently I am going through Normal Equation in Machine Learning. $$\hat\theta = (X^T \cdot X)^{-1} \cdot X^T \cdot y$$ But when I see how they use this equation, I found they always add an ...
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### Deriving backpropagation equations "natively" in tensor form

Image shows a typical layer somewhere in a feed forward network: $a_i^{(k)}$ is the activation value of the $i^{th}$ neuron in the $k^{th}$ layer. $W_{ij}^{(k)}$ is the weight connecting $i^{th}$ ...
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### Closed form solution of linear regression via least squares using matrix derivatives

How is the closed form solution to linear regression derived using matrix derivatives as opposed to using the trace method as Andrew Ng does in his Machine learning lectures. Specifically, I am ...
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### How is image convolution actually implemented in deep learning libraries using simple linear algebra?

As a clarifier, I want to implement cross-correlation, but the machine learning literature keeps referring to it as convolution so I will stick with it. I am trying to implement image convolution ...
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### Mathematical formulation of Support Vector Machines?

I'm trying to learn maths behind SVM (hard margin) but due to different forms of mathematical formulations I'm bit confused. Assume we have two sets of points $\text{(i.e. positives, negatives)}$ one ...
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### What type of technique can be used to solve this question?

Apology for the ambiguous title, I do not know the term. I have data of some products which a few variables: origin, weight, brand. For example: Product A = "China, 100g, Brand X" Product ...
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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 does np.linalg.eig produce an opposite-signed eigenvector?

I am learning SVD by following this MIT course. In this video, the lecturer is finding the SVD for $$\begin{pmatrix} 5 & 5 \\ -1 & 7 \end{pmatrix},$$ which involves finding the ...
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### 3d input for Dense Layer Keras

Is there any example of how Keras Dense layer handles 3D input. The documentation explains the following: ...
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### Difference between FDA and LDA

I have asked this question in Mathematics Stackexchange, thought however that it might be more fit for here: I am currently taking a Data-Analysis course and I learned about both the terms LDA (Linear ...
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