# 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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### Covariance matrix square root

Consider a random variable $r_t$ which represents the return of an asset at time t. In the univariate case, we just consider $r_t$ to be the return of a single security at time t. Generally, we assume ...
10 views

### trying to create a cache dataset in monai: LinAlgError: SVD did not converge [closed]

This is the error that I am getting: ...
673 views

35 views

### Johansen test accepts first null hypothesis but would reject last one

Suppose that we perfrom a Johansen test over three I(1) variables that give us these results through the maximum eigenvalues statistic: as you can see, we accept the null hypothesis in the first step ...
1 vote
25 views

### Least Squares Regression with Length and Density of input data

I have a collection of data that I expect to be linear but has a unknown amount of noise to the data. Initially I wanted to use the least squares regression line to determine if the slope, y axis, and ...
210 views

1 vote
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### Calculating initial values of a Linear Regression Model

I have the following problem Given the training data for a linear regresison problem as follow: Input Output 0 0 1 2 -1 -2 2 3 After the first iteration, the values of the two coefficients are ...
1 vote
98 views

### Deriving vectorized back propagation

I'm trying to derive vectorized backpropagation from mostly first principles, but I'm having trouble marrying how this paper explains backpropagation with the derivative of a loss function with ...
103 views

### Intuition behind rank of covariance matrix and testing hypotheses

I am trying to acquire some intuition about testing multivariate hypotheses where the test statistic involves inverse covariance matrix. As an example, suppose we have a $p$-variate random vector that ...
1 vote
47 views

Studying NN and I wanted to grasp from scratch the theory of gradient descent and matrices derivatives, so I took a simple scenario and tried to apply gradient ascent and see if everything made sense. ...
34 views

### Eigenvalues of a block matrix

Let $\bar{\lambda}$ be the smallest eigenvalue of $$M=\Omega^{-1/2}Y'Z(Z'Z)^{-1}Z'Y\Omega^{-1/2}$$, where $\Omega$, $Y$, and $Z$ are $(l\times l)$, $(N\times l)$, and $(N \times k)$ matrices, ...
53 views

1 vote