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37 votes
17 answers
13k views

Listing applications of the SVD

The SVD (singular value decomposition) is taught in many linear algebra courses. It's taken for granted that it's important. I have helped teach a linear algebra course before, and I feel like I need ...
5 votes
1 answer
539 views

Under what circumstances Is a symmetric matrix representable as a Coulomb matrix?

Question: I am exploring a neural network architecture inspired by physical interactions, where each neuron has associated "mass" and "position" vectors. The weight matrix between ...
mathoverflowUser's user avatar
3 votes
4 answers
6k views

Applied linear algebra textbook? [closed]

I have a copy of Linear Algebra Done Right, which I worked through years ago in college. I have been using that book to refresh my knowledge, but it does not have an applied or computational aspect ...
dkh's user avatar
  • 33
1 vote
1 answer
348 views

General strategy of error bound of matrix exponential

I want to ask General strategy of the error bound of the matrix exponential. For example, suppose, $A, B$ are finite dimension $n \times n$ matrices with complex coefficients. Using Baker–Campbell–...
En-Jui Kuo's user avatar
1 vote
0 answers
46 views

Regression models as local sections of a chain complex

Let's say we find some regression equation $\ell$ (best fit / linear / whatever words you need to put here) for a sample $D$, subset of population $P$. This equation/model can be thought of as a ...
cheyne's user avatar
  • 1,611
0 votes
1 answer
87 views

Finding a vector representation for a data where we only know the inner products

I am an engineer working on speech signal processing and I have a problem that I have encountered while trying to model speech signals. The mathematical formulation is not entirely pure and I try to ...
Rajesh D's user avatar
  • 698
0 votes
0 answers
36 views

Conjugate gradient-like algorithm with multiple search directions

I am solving an $n*n$ system $Ax=b$ in CUDA where $A$ is a sparse matrix. Currently I am solving it using the conjugate gradient algorithm. I have noticed that $Ax$ where $x$ is $n*1$ has roughly the ...
SRB121's user avatar
  • 71
0 votes
0 answers
608 views

Orthogonal Projections in Lie Theory

I have been studying a finite element method where rigid & elastic spatial motions are separated using an orthogonal projection (actually two: one for translations/stretches, the other for ...
John Craighead's user avatar
-2 votes
1 answer
213 views

Solving a difficult equation for a variable?

I'm trying to obtain the maximum likelihood estimate of the parameters for a model I'm building. I have constants $\sigma$, $\mu$, and $q_0$; a boolean matrix $\alpha$; and vectors $A, \beta, r, d,$ ...
rhombidodecahedron's user avatar