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Everything about Permutation matrix
Matrix with exactly one 1 per row and column
In mathematics, particularly in matrix theory, a permutation matrix is a square binary matrix that has exactly one entry of 1 in each row and each column with all other entries 0. An n × n permutation matrix can represent a permutation of n elements. Pre-multiplying an n-row matrix M by a permutation matrix P, forming PM, results in permuting the rows of M, while post-multiplying an n-column matrix M, forming MP, permutes the columns of M. Wikipedia →
🧠Start here: a 6-step reading path
- Read the overview: Permutation matrixA 5-minute orientation
- Skim a recent paper: End-to-End Learning the Partial Permutation Matrix for Robust 3D Point Cloud RegistrationInfluential work since 2022
- Pick up a classic book: Black box classical groupsThe most-reprinted book on the subject
- Read the landmark paper: Algorithm 230: Matrix PermutationCited 337 times
- Go sideways: Laplace expansionA closely related topic
- Go sideways: Singular value decompositionA closely related topic
đź“– Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
Algorithm 230: Matrix Permutation
Image encryption based on three-dimensional bit matrix permutation
Permutation symmetries and the fermion mass matrix
The use of the vec-permutation matrix in spatial matrix population models
An investigation of three-matrix permutation tests
Erratum: Permutation symmetries and the fermion mass matrix
Matrix factorisations and permutation branes
Permutation branes and linear matrix factorisations
🆕 Influential since 2022
End-to-End Learning the Partial Permutation Matrix for Robust 3D Point Cloud Registration
Privacy-Preserving Image Classification Using ConvMixer with Adaptative Permutation Matrix and Block-Wise Scrambled Image Encryption
Lightweight symmetric key encryption for text using XOR operation and permutation matrix
Matrix operations in Random Permutation Set
Partial Permutation and Alternating Sign Matrix Polytopes
đź“š Books worth reading
- 📕Black box classical groupsW. M. Kantor · 2001
Black box classical groupsWilliam M. Kantor, Akos Seress · 2001- 📕Linear Algebra IFrederick P. Greenleaf, Sophie Marques · 2019
- 📕Algebraic design theoryWarwick De Launey · 2011
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
đź”— Related topics
- Laplace expansion In linear algebra, the Laplace expansion, named after Pierre-Simon Laplace, also called cofactor expansion, is an expression of the determinant of an n…
- Singular value decomposition In linear algebra, the singular value decomposition (SVD) is a factorization of a real or complex matrix into a rotation, followed by a scaling, followed…
- Permanent (mathematics) In linear algebra, the permanent of a square matrix is a function of the matrix similar to the determinant. The permanent, as well as the determinant,…
- LU decomposition In numerical analysis and linear algebra, lower–upper (LU) decomposition or factorization factors a matrix as the product of a lower triangular matrix…
- Computing the permanent In linear algebra, the computation of the permanent of a matrix is a problem that is thought to be more difficult than the computation of the determinant…
- Cauchy–Binet formula In mathematics, specifically linear algebra, the Cauchy–Binet formula, named after Augustin-Louis Cauchy and Jacques Philippe Marie Binet, is an identity…
- Permutation In mathematics, a permutation is a bijective function of a finite set onto itself. When the set is represented as an ordered sequence of its members, a…
- Generalized permutation matrix In mathematics, a generalized permutation matrix (or monomial matrix) is a matrix with the same nonzero pattern as a permutation matrix, i.e. there is…