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Everything about Matrix decomposition
Representation of a matrix as a product
In the mathematical discipline of linear algebra, a matrix decomposition or matrix factorization is a factorization of a matrix into a product of matrices. There are many different matrix decompositions; each finds use among a particular class of problems. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Matrix decompositionA 5-minute orientation
- Skim a recent paper: Decomposition of matrix product states into shallow quantum circuitsInfluential work since 2022
- Pick up a classic book: Mathematics for Machine LearningThe most-reprinted book on the subject
- Read the landmark paper: Finding Structure with Randomness: Probabilistic Algorithms for Constructing Approximate Matrix DecompositionsCited 3,026 times
- Go sideways: Symmetric matrixA closely related topic
- Go sideways: Skew-Hermitian matrixA closely related topic
📖 Definitions
Noun A process by which a matrix (a rectangular table of numbers or abstract quantities that can be added and multiplied) is broken down into simpler numerical building blocks.
🏆 Landmark papers (most cited)
Finding Structure with Randomness: Probabilistic Algorithms for Constructing Approximate Matrix Decompositions
Rank-Sparsity Incoherence for Matrix Decomposition
Mueller matrix differential decomposition
Complex Matrix Decomposition and Quadratic Programming
Robust Matrix Decomposition With Sparse Corruptions
A Generalized Least-Square Matrix Decomposition
Optical matrix–matrix multiplier based on outer product decomposition
A matrix decomposition and its applications
🆕 Influential since 2022
Decomposition of matrix product states into shallow quantum circuits
Modelling matrix time series via a tensor CP-decomposition
RMMLP:Rolling MLP and matrix decomposition for skin lesion segmentation
Joint matrix decomposition for deep convolutional neural networks compression
A Generalized CUR Decomposition for Matrix Pairs
📚 Books worth reading
Mathematics for Machine LearningMarc Peter Deisenroth, A. Aldo Faisal · 2019
Projection Matrices, Generalized Inverse Matrices, and Singular Value DecompositionHaruo Yanai · 2011
Тензорная тригонометрияNinul Anatoly Sergeevich · 2004
Matrix DecompositionsAndrew Kloczkowski · 2022
Jordan canonical formSteven H. Weintraub · 2008
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Symmetric matrix In linear algebra, a symmetric matrix is a square matrix that is equal to its transpose. Formally, A is symmetric ⟺ A = A T . {\displaystyle A{\text{…
- Skew-Hermitian matrix In linear algebra, a square matrix with complex entries is said to be skew-Hermitian or anti-Hermitian if its conjugate transpose is the negative of the…
- Square root of a matrix In mathematics, the square root of a matrix extends the notion of square root from numbers to matrices. A matrix B is said to be a square root of A if…
- Schur decomposition In linear algebra, the Schur decomposition or Schur triangulation, named after Issai Schur, is a matrix decomposition. It allows one to write an arbitrary…
- Sylvester's law of inertia Sylvester's law of inertia is a theorem in matrix algebra about certain properties of the coefficient matrix of a real quadratic form that remain invariant…
- Numerical linear algebra Numerical linear algebra, sometimes called applied linear algebra, is the study of how matrix operations can be used to create computer algorithms which…
- Eigendecomposition of a matrix In linear algebra, eigendecomposition (also known as eigenvalue decomposition or EVD) is a factorization of a matrix A into a canonical form given by A=QDQ−𝟣…
- Hessenberg matrix In linear algebra, a Hessenberg matrix is a special kind of square matrix, one that is "almost" triangular. To be exact, an upper Hessenberg matrix has…