190 citations · 210 across the 8 of their papers we have counts for
8 papers
The Pseudoinverse of is (?)
Michał P. Karpowicz, Gilbert Strang
This paper gives three formulas for the pseudoinverse of a matrix product . The first is sometimes correct, the second is always correct, and the third is almost never corr…
Elimination and Factorization
Gilbert Strang
If a matrix has rank , then its row echelon form (from elimination) contains the identity matrix in its first independent columns. How do we \emph{interpret the matrix}…
A Neural Network Solves, Explains, and Generates University Math Problems by Program Synthesis and Few-Shot Learning at Human Level
Iddo Drori, Sarah Zhang, Reece Shuttleworth +15
We demonstrate that a neural network pre-trained on text and fine-tuned on code solves mathematics course problems, explains solutions, and generates new questions at a human level…
A Local Inverse Formula and a Factorization
Gilbert Strang, Shev MacNamara
When a matrix has a banded inverse there is a remarkable formula that quickly computes that inverse, using only local information in the original matrix. This local inverse formula…
Random Triangle Theory with Geometry and Applications
Alan Edelman, Gilbert Strang
What is the probability that a random triangle is acute? We explore this old question from a modern viewpoint, taking into account linear algebra, shape theory, numerical analysis,…
The Green's Function for the Hückel (Tight Binding) Model
Ramis Movassagh, Gilbert Strang, Yuta Tsuji +1
Applications of the Hückel (tight binding) model are ubiquitous in quantum chemistry and solid state physics. The matrix representation of this model is isomorphic to an unoriented…
The Main Diagonal of a Permutation Matrix
Marko Lindner, Gilbert Strang
By counting 1's in the "right half" of consecutive rows, we locate the main diagonal of any doubly infinite permutation matrix with bandwidth . Then the matrix can be corre…
Wavelet transforms versus Fourier transforms
Gilbert Strang
This note is a very basic introduction to wavelets. It starts with an orthogonal basis of piecewise constant functions, constructed by dilation and translation. The ``wavelet trans…