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Everything about Matrix ring
Mathematical ring whose elements are matrices
In abstract algebra, a matrix ring is a set of matrices with entries in a ring R that form a ring under matrix addition and matrix multiplication. The set of all n × n matrices with entries in R is a matrix ring denoted Mn(R) (alternative notations: M(n, R), Matn(R) and Rn×n). Some sets of infinite matrices form infinite matrix rings. A subring of a matrix ring is again a matrix ring. Over a rng, one can form matrix rngs. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Matrix ringA 5-minute orientation
- Skim a recent paper: Discovering faster matrix multiplication algorithms with reinforcement learningInfluential work since 2022
- Pick up a classic book: Algebras, rings and modulesThe most-reprinted book on the subject
- Read the landmark paper: Tests for comparing elements of a correlation matrix.Cited 3,919 times
- Go sideways: Glossary of ring theoryA closely related topic
- Go sideways: Ring (mathematics)A closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Tests for comparing elements of a correlation matrix.
Matrix metalloproteinase-9 triggers the angiogenic switch during carcinogenesis
Triangular matrix representations of ring extensions
Low Tensor-Ring Rank Completion by Parallel Matrix Factorization
Communication Over Finite-Chain-Ring Matrix Channels
THE GROUP OF GRAPH AUTOMORPHISMS OVER A MATRIX RING
Properly integral polynomials over the ring of integer-valued polynomials on a matrix ring
A matrix ring description for cyclic convolutional codes
🆕 Influential since 2022
Discovering faster matrix multiplication algorithms with reinforcement learning
Decellularized extracellular matrix scaffolds: Recent trends and emerging strategies in tissue engineering
Recent progress on the additive manufacturing of aluminum alloys and aluminum matrix composites: Microstructure, properties, and applications
Tissue extracellular matrix hydrogels as alternatives to Matrigel for culturing gastrointestinal organoids
Immunogenicity of decellularized extracellular matrix scaffolds: a bottleneck in tissue engineering and regenerative medicine
📚 Books worth reading
Algebras, rings and modulesMichiel Hazewinkel, Nadiya Gubareni · 2004
Theory of generalized inverses over commutative ringsK. P. S. Bhaskara Rao · 2002
Skew linear groupsM. Shirvani · 1986
AlgèbreN. Bourbaki · 2007
Groups, Rings, Lie and Hopf AlgebrasY. Bahturin · 2003
The Linear Algebra - A Beginning Graduate Student Ought to Know (Texts in the Mathematical Sciences)Jonathan S. Golan · 2004
Linear Algebra and GeometryIgor R. Shafarevich · 2013- 📕AlgebraSerge Lang · 2012
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
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