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Everything about Matrix multiplication
Mathematical operation in linear algebra
In mathematics, specifically in linear algebra, matrix multiplication is a binary operation that produces a matrix from two matrices. For matrix multiplication, the number of columns in the first matrix must be equal to the number of rows in the second matrix. The resulting matrix, known as the matrix product, has the number of rows of the first and the number of columns of the second matrix. The product of matrices A and B is denoted as AB. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Matrix multiplicationA 5-minute orientation
- Skim a recent paper: Photonic matrix multiplication lights up photonic accelerator and beyondInfluential work since 2022
- Pick up a classic book: Introduction to Multiple Time Series AnalysisThe most-reprinted book on the subject
- Read the landmark paper: CLUSTAL W: improving the sensitivity of progressive multiple sequence alignment through sequence weighting, position-specific gap penalties and weight matrix choiceCited 52,868 times
- Go sideways: TransposeA closely related topic
- Go sideways: Outer productA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
CLUSTAL W: improving the sensitivity of progressive multiple sequence alignment through sequence weighting, position-specific gap penalties and weight matrix choice
Matrix multiplication via arithmetic progressions
Fast sparse matrix multiplication
Partial and Total Matrix Multiplication
Matrix multiplication on heterogeneous platforms
Rectangular Matrix Multiplication Revisited
Compressed matrix multiplication
Matrix Multiplication by Optical Methods
🆕 Influential since 2022
Photonic matrix multiplication lights up photonic accelerator and beyond
Discovering faster matrix multiplication algorithms with reinforcement learning
A Systematic Survey of General Sparse Matrix-matrix Multiplication
Coherent Photonic Crossbar Arrays for Large-Scale Matrix-Matrix Multiplication
DGEMM on integer matrix multiplication unit
📚 Books worth reading
Introduction to Multiple Time Series AnalysisHelmut Lütkepohl, Helmut Lutkepohl · 1991- 📕Satellite-matrix-switched, time-division-multiple-access network simulatorWilliam D. Ivancic · 1989
- 📕Computer-aided discovery of a fast matrix-multiplication algorithmRodney W. Johnson · 1979
- 📕Computer-aided discovery of a fast matrix-multiplication algorithmRodney W Johnson · 1979
Coding the MatrixPhilip N. Klein · 2013- 📕Satellite range delay simulator for a matrix-switched time division multiple-access network simulatorLawrence A. Nagy · 1990
- 📕Algorithms for matrix multiplicationR. P. Brent · 1970
- 📕Fast Matrix Multiplication with ApplicationsJerzy S. Respondek · 2025
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Transpose In linear algebra, transposition is an operation that flips a matrix over its diagonal; that is, transposition switches the row and column indices of the…
- Outer product In linear algebra, the outer product of two coordinate vectors is the matrix whose entries are all products of an element in the first vector with an element…
- Determinant In mathematics, the determinant is a scalar-valued function of the entries of a square matrix that has many properties which make it fundamental for the…
- Matrix (mathematics) In mathematics, a matrix (pl.: matrices) is a rectangular array of numbers or other mathematical objects with elements or entries arranged in rows and…
- Dot product In mathematics, the dot product is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors), and returns a…
- Hermitian matrix In mathematics, a Hermitian matrix (or self-adjoint matrix) is a square matrix with complex-valued entries that is equal to its own conjugate transpose…
- Moore–Penrose inverse In mathematics, and in particular linear algebra, the Moore–Penrose inverse A+ of a matrix A, often called the pseudoinverse, is the most widely known…
- Block matrix In mathematics, a block matrix or a partitioned matrix is a matrix that is interpreted as having been broken into sections called blocks or submatrices…