Search for "Matrices" in article titles:

1. Matrices of binary remainders: Research Project: The object is: to be able to distinguish a prime by what it is rather than by what it is not, using purely linear algebraic processes. to be able to factorize a composite into its prime factors not ... [100%] 2023-12-27
2. Expressing Linear Equations As Matrices: This page contains practice exercises for expressing linear equations as matrices. [89%] 2023-03-05 [Equations]
3. Transitional Matrices of Binary Remainders: Transitional Matrices of Binary Remainders [Cyclic Quality]. [The following is research, but since this is essentially elementary mathematics, the content of this contribution may be considered as self-validating.] The matrices represent uneven integers exclusively. [89%] 2023-04-01
4. Williamson matrices: A Hadamard matrix of order $n$ is an $( n \times n )$-matrix $H$ with entries $+ 1$ and $- 1$ such that $H H ^ { T } = H ^ { T } H = n I _ { n }$, where $H ^ { T }$ is the transposed matrix of $H$ and ... (Mathematics) [100%] 2023-11-14
5. Pauli matrices: In mathematical physics and mathematics, the Pauli matrices are a set of three 2 × 2 complex matrices which are Hermitian, involutory and unitary. Usually indicated by the Greek letter sigma (σ), they are occasionally denoted by tau (τ) when used in connection ... (Matrices important in quantum mechanics and the study of spin) [100%] 2024-01-11 [Lie groups] [Matrices]...
6. Equivalent matrices: $A$ and $B$ over a ring $R$ Matrices such that $A$ can be transformed into $B$ by a sequence of elementary row-and-column transformations, that is, transformations of the following three types: a) permutation of the rows (or columns ... (Mathematics) [100%] 2023-10-17
7. Similar matrices: Square matrices $A$ and $B$ of the same order related by $B=S^{-1}AS$, where $S$ is a non-singular matrix of the same order. Similar matrices have the same rank, the same determinant, the same characteristic polynomial, and ... (Mathematics) [100%] 2023-12-28 [Linear and multilinear algebra] [ matrix theory]...
8. Pauli matrices: Certain special constant Hermitian $ ( 2 \times 2) $-matrices with complex entries. They were introduced by W. (Mathematics) [100%] 2023-10-17
9. Dirac matrices: Four Hermitian matrices, denoted by $ \alpha_{1} $, $ \alpha_{2} $, $ \alpha_{3} $ and $ \beta $, of dimension $ 4 \times 4 $ that satisfy the relations \begin{gather} \alpha_{k} \alpha_{j} + \alpha_{j} \alpha_{k} = 2 \delta_{k j} \mathsf{I}_{4 ... (Mathematics) [100%] 2023-10-19
10. Perinatal matrices: Perinatal matrices or basic perinatal matrices, in pre-perinatal and transpersonal psychology, is a theoretical model of describing the state of awareness before and during birth. [100%] 2023-11-27 [New Age practices]
11. Congruent matrices: Matrices $A$, $B$ over a ring $R$ for which there exists an invertible matrix $P$ such that $B = P^t A P$, where $P^t$ denotes the transposed matrix of $P$. Congruence of matrices is an equivalence relation. (Mathematics) [100%] 2023-11-14
12. Pauli matrices: In physics, the Pauli matrices are a set of 2 × 2 complex Hermitian and unitary matrices. Usually indicated by the Greek letter "sigma" (σ), they are occasionally denoted with a "tau" (τ) when used in connection with isospin symmetries. [100%] 2023-12-28 [Lie groups] [Matrices]...
13. Pauli matrices: In mathematical physics and mathematics, the Pauli matrices are a set of three 2 × 2 complex matrices that are Hermitian, involutory and unitary. Usually indicated by the Greek letter sigma (σ), they are occasionally denoted by tau (τ) when used in connection ... (Matrices important in quantum mechanics and the study of spin) [100%] 2024-03-29 [Lie groups] [Matrices]...
14. Gell-Mann matrices: The Gell-Mann matrices, developed by Murray Gell-Mann, are a set of eight linearly independent 3×3 traceless Hermitian matrices used in the study of the strong interaction in particle physics. They span the Lie algebra of the SU ... (Physics) [81%] 2023-01-29 [Matrices] [Quantum chromodynamics]...
15. Weyl–Brauer matrices: In mathematics, particularly in the theory of spinors, the Weyl–Brauer matrices are an explicit realization of a Clifford algebra as a matrix algebra of 2 × 2 matrices. They generalize the Pauli matrices to n dimensions, and are a specific ... (Matrix realization of the Clifford algebra) [81%] 2022-11-23 [Spinors] [Matrices]...
16. Gell-Mann matrices: The Gell-Mann matrices are denoted by $ \lambda _ {1} \dots \lambda _ {8} $. They form a family of traceless Hermitian $ ( 3 \times 3 ) $- matrices, orthonormalized as follows: $ { \mathop{\rm Tr} } ( \lambda _ {j} \lambda _ {k} ) = 2 \delta _ ... (Mathematics) [81%] 2023-06-24
17. Gell-Mann matrices: The Gell-Mann matrices, developed by Murray Gell-Mann, are a set of eight linearly independent 3×3 traceless Hermitian matrices used in the study of the strong interaction in particle physics. They span the Lie algebra of the SU ... (A basis for the SU(3) Lie algebra) [81%] 2023-12-03 [Matrices] [Quantum chromodynamics]...
18. Pauli spin matrices: The Pauli spin matrices (named after physicist Wolfgang Ernst Pauli) are a set of unitary Hermitian matrices which form an orthogonal basis (along with the identity matrix) for the real Hilbert space of 2 × 2 Hermitian matrices and for the ... [81%] 2023-06-14
19. Category of matrices: In mathematics, the category of matrices, often denoted M a t {\displaystyle \mathbf {Mat} } , is the category whose objects are natural numbers and whose morphisms are matrices, with composition given by matrix multiplication. Let A {\displaystyle A} be an n ... (Basic definition and properties of the category of matrices) [81%] 2024-07-16 [Categories in category theory] [Linear algebra]...
20. Higher-dimensional gamma matrices: In mathematical physics, higher-dimensional gamma matrices generalize to arbitrary dimension the four-dimensional Gamma matrices of Dirac, which are a mainstay of relativistic quantum mechanics. They are utilized in relativistically invariant wave equations for fermions (such as spinors) in ... (Gamma matrices for arbitrary Clifford algebras) [70%] 2023-07-07 [Spinors] [Matrices]...
21. Distance matrices in phylogeny: Distance matrices are used in phylogeny as non-parametric distance methods and were originally applied to phenetic data using a matrix of pairwise distances. These distances are then reconciled to produce a tree (a phylogram, with informative branch lengths). (Matrices used in construction of phylogenetic trees) [70%] 2023-12-16 [Computational phylogenetics]
22. Explicit binary remainder matrices: Research Project: SQUARE NON-SINGULAR MATRICES CONTAINING BINARY REMAINDERS AS ELEMENTS ASSOCIATED WITH TWO RAISED TO THE APPROPRIATE BINARY PLACE VALUE. The Division Algorithm with divisor two is usually written: Q[n, N] is an uneven integer defined by Q ... [70%] 2023-04-09 [Mathematics]
23. Normal form (for matrices): The normal form of a matrix $ A $ is a matrix $ N $ of a pre-assigned special form obtained from $ A $ by means of transformations of a prescribed type. One distinguishes various normal forms, depending on the type of transformations in ... (Mathematics) [70%] 2023-10-17
24. Generalizations of Pauli matrices: In mathematics and physics, in particular quantum information, the term generalized Pauli matrices refers to families of matrices which generalize the (linear algebraic) properties of the Pauli matrices. Here, a few classes of such matrices are summarized. [70%] 2023-09-14 [Linear algebra] [Mathematical physics]...
25. Higher-dimensional gamma matrices: In mathematical physics, higher-dimensional gamma matrices generalize to arbitrary dimension the four-dimensional Gamma matrices of Dirac, which are a mainstay of relativistic quantum mechanics. They are utilized in relativistically invariant wave equations for fermions (such as spinors) in ... (Physics) [70%] 2022-06-10 [Quantum field theory] [Spinors]...
26. Duplication and elimination matrices: In mathematics, especially in linear algebra and matrix theory, the duplication matrix and the elimination matrix are linear transformations used for transforming half-vectorizations of matrices into vectorizations or (respectively) vice versa. The duplication matrix \displaystyle{ D_n }[/math] is the ... [70%] 2023-08-20 [Matrices]
27. Trigonometric functions of matrices: The trigonometric functions (especially sine and cosine) for real or complex square matrices occur in solutions of second-order systems of differential equations. They are defined by the same Taylor series that hold for the trigonometric functions of real and ... (Important functions in solving differential equations) [70%] 2024-07-27 [Trigonometry] [Matrix theory]...
28. Representation of matrices, problem of: problem of presentation of matrices The problem of whether one can exhibit a unified general method (an algorithm) that would give, in a finite number of steps, an answer to the question whether a matrix $U$ can be represented by ... (Mathematics) [63%] 2023-10-18
29. Partially specified matrices, completion of: A partially specified $ ( p \times q ) $-matrix is a $ ( p \times q ) $-array of complex numbers (or, more generally, of elements over an arbitrary field) in which certain entries are given and the other entries are not specified. The latter ... (Mathematics) [63%] 2023-10-25
30. Binarization of consensus partition matrices: Mainly in the context of gene clustering, the binarization of consensus partition matrices (Bi-CoPaM) was proposed by Abu-Jamous et al. as a method for consensus clustering. [63%] 2024-08-20 [Cluster analysis algorithms] [Statistical algorithms]...