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Matrix which differs from the identity matrix by one elementary row operation
an elementary matrix is a square matrix obtained from the application of a single elementary row operation to the identity matrix. The elementary matrices
Elementary_matrix
Matrix defined using smaller matrices called blocks
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
Block_matrix
Square matrix with ones on the main diagonal and zeros elsewhere
Binary matrix (zero-one matrix) Elementary matrix Exchange matrix Matrix of ones Pauli matrices (the identity matrix is the zeroth Pauli matrix) Householder
Identity_matrix
Square matrix which is its own inverse
classes of elementary matrix is involutory, namely the row-interchange elementary matrix. A special case of another class of elementary matrix, that which
Involutory_matrix
Form of a matrix
linear algebra, a skew-symmetric (or antisymmetric or antimetric) matrix is a square matrix whose transpose equals its negative. That is, it satisfies the
Skew-symmetric_matrix
Algorithm for solving systems of linear equations
invertible matrix. The method is named after Carl Friedrich Gauss (1777–1855). To perform row reduction on a matrix, one uses a sequence of elementary row operations
Gaussian_elimination
Matrix with a multiplicative inverse
algebra, an invertible matrix (non-singular, non-degenerate or regular) is a square matrix that has an inverse. In other words, if a matrix is invertible, it
Invertible_matrix
Type of geometric transformation
a shear matrix or transvection, an elementary matrix that represents the addition of a multiple of one row or column to another. Such a matrix may be derived
Shear_mapping
Matrix whose only nonzero elements are on its main diagonal
In linear algebra, a diagonal matrix is a matrix in which the entries outside the main diagonal are all zero; the term usually refers to square matrices
Diagonal_matrix
Array of numbers
In mathematics, a matrix (pl.: matrices) is a rectangular array of numbers or other mathematical objects with elements or entries arranged in rows and
Matrix_(mathematics)
Matrix whose only nonzero entries lie on the lower-left-to-upper-right diagonal
In mathematics, an anti-diagonal matrix is a square matrix where all the entries are zero except those on the diagonal going from the lower left corner
Anti-diagonal_matrix
For a square matrix, the transpose of the cofactor matrix
classical adjoint adj(A) of a square matrix A is the transpose of its cofactor matrix. It is occasionally known as adjunct matrix, or "adjoint", though that normally
Adjugate_matrix
A Frobenius matrix is a special kind of square matrix from numerical analysis. A matrix is a Frobenius matrix if it has the following three properties:[citation
Frobenius_matrix
Dimension of the column space of a matrix
approach to finding the rank of a matrix is to reduce it to a simpler form, generally row echelon form, by elementary row operations. Row operations do
Rank_(linear_algebra)
Determinant of a subsection of a square matrix
In linear algebra, a minor of a matrix A is the determinant of some smaller square matrix generated from A by removing one or more of its rows and columns
Minor_(linear_algebra)
Type of topological space
one replaces Tietze moves for the fundamental group presentation by elementary matrix operations for the presentation matrices for H n ( X ; Z ) {\displaystyle
CW_complex
Possible form of a matrix
column. The reduced row echelon form of a matrix is unique and does not depend on the sequence of elementary row operations that is used to obtain it.
Row_echelon_form
Equivalence under a change of basis (linear algebra)
the elementary divisors of A; these can be immediately read off from a matrix in Jordan form, but they can also be determined directly for any matrix by
Matrix_similarity
Topics referred to by the same term
association Ecosia, web search engine Elementary column operations, performed on the columns of an elementary matrix in mathematics Engineering change order
Eco
Complex matrix whose conjugate transpose equals its inverse
In linear algebra, an invertible complex square matrix U is unitary if its matrix inverse U−1 equals its conjugate transpose U*, that is, if U ∗ U = U
Unitary_matrix
Matrix in math with special properties
In mathematics, a conference matrix (also called a C-matrix) is a square matrix C with 0 on the diagonal and +1 and −1 off the diagonal, such that CTC
Conference_matrix
Mathematical operation
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 the matrix product BB is
Square_root_of_a_matrix
Real square matrix whose columns and rows are orthogonal unit vectors
In linear algebra, an orthogonal matrix or orthonormal matrix Q, is a real-valued square matrix whose columns and rows are orthonormal vectors. One way
Orthogonal_matrix
Branch of mathematics
University Press. ISBN 978-0-19-283098-2. Hohn, Franz E. (2013). Elementary Matrix Algebra. Dover Publications. ISBN 978-0-486-14372-9. Houston, Stephen
Algebra
Matrix representing a Euclidean rotation
rotation matrix is a transformation matrix that is used to perform a rotation in Euclidean space. For example, using the convention below, the matrix R = [
Rotation_matrix
Equivalence of matrices under row operations
of elementary row operations. The row space of a matrix is the set of all possible linear combinations of its row vectors. If the rows of the matrix represent
Row_equivalence
Matlab and Scilab. It aims at providing finite element methods and elementary matrix computations for solving linear and non-linear problems numerically
GetFEM++
Mathematical operation
pp. 536, 7, ISBN 978-0-471-50447-4 Ch.VII, §7.2 Howard Eves (1966) Elementary Matrix Theory, § 5.4A Cayley’s Construction of Real Orthogonal Matrices,
Cayley_transform
matrices used in mathematics, science and engineering. A matrix (plural matrices, or less commonly matrixes) is a rectangular array of numbers called entries
List_of_named_matrices
Property of a mathematical matrix
definiteness of a symmetric real matrix. Namely, the matrix is reduced to an upper triangular matrix by using elementary row operations, as in the first
Definite_matrix
Topics referred to by the same term
operator in genetic algorithms Elementary row operations, an operation performed on the rows of an elementary matrix in mathematics Ero (spider), a genus
ERO
{\displaystyle {\mathsf {ELEMENTARY}}} consists of the decision problems that can be solved in time bounded by an elementary recursive function. Equivalently
ELEMENTARY
Matrix equal to its conjugate-transpose
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
Hermitian_matrix
Group of matrices with determinant 1
Let T i j := e i j ( 1 ) {\displaystyle T_{ij}:=e_{ij}(1)} be the elementary matrix with 1 {\displaystyle 1} 's on the diagonal and in the i j {\displaystyle
Special_linear_group
Binary arithmetic algorithm
values, so 1 + 1 = 0 {\displaystyle 1+1=0} ), which expresses the elementary matrix of switching two rows (or columns) in terms of the transvections (shears)
XOR_swap_algorithm
Form of a matrix indicating its eigenvalues and their algebraic multiplicities
converse is not true. This leads to the notion of elementary divisors. The elementary divisors of a square matrix A are the characteristic polynomials of its
Jordan_normal_form
Matrix formed by appending columns of two other matrices
-dimensional matrix A {\displaystyle A} . This is usually done for the purpose of performing the same elementary row operations on the augmented matrix ( A |
Augmented_matrix
American filmmakers
The Matrix (1999), a major box-office success for which they won the Saturn Award for Best Director. They wrote and directed two sequels, The Matrix Reloaded
The_Wachowskis
Branch of mathematics
and only if one can transform one into the other by elementary row and column operations. For a matrix representing a linear map from W to V, the row operations
Linear_algebra
In mathematics, invariant of square matrices
square matrix. The determinant of a matrix A is commonly denoted det(A), det A, or |A|. Its value characterizes some properties of the matrix and the
Determinant
Unitary matrix containing information on the weak interaction
physics, the Cabibbo–Kobayashi–Maskawa matrix, CKM matrix, quark mixing matrix, or KM matrix is a unitary matrix that contains information on the strength
Cabibbo–Kobayashi–Maskawa matrix
Cabibbo–Kobayashi–Maskawa_matrix
Matrices similar to diagonal matrices
linear algebra, a square matrix A {\displaystyle A} is called diagonalizable or non-defective if it is similar to a diagonal matrix. That is, if there exists
Diagonalizable_matrix
Matrix of geometric progressions
In linear algebra, a Vandermonde matrix, named after Alexandre-Théophile Vandermonde, is a matrix with the terms of a geometric progression in each row:
Vandermonde_matrix
Matrix operation generalizing exponentiation of scalar numbers
In mathematics, the matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function. It is used to solve systems
Matrix_exponential
Subatomic particle having no substructure
In the Standard Model of particle physics, an elementary particle or fundamental particle is a subatomic particle that is not composed of other particles
Elementary_particle
Vector spaces associated to a matrix
range or image) of a matrix A is the span (set of all possible linear combinations) of its column vectors. The column space of a matrix is the image or range
Row_and_column_spaces
Mathematical operation on invertible matrices
mathematics, a logarithm of a matrix is another matrix such that the matrix exponential of the latter matrix equals the original matrix. It is thus a generalization
Logarithm_of_a_matrix
Mathematics concept
In mathematics, a Hadamard matrix, named after the French mathematician Jacques Hadamard, is a square matrix whose entries are either +1 or −1 and whose
Hadamard_matrix
_{i=1}^{n}e_{ij}\otimes e_{ji}} , where e i j {\displaystyle e_{ij}} denotes the elementary matrix which is 0 except for the entry in the (i, j) entry, which is 1. In
Separable_algebra
Model of neutrino oscillation
matrix (PMNS matrix), Maki–Nakagawa–Sakata matrix (MNS matrix), lepton mixing matrix, or neutrino mixing matrix is a unitary mixing matrix that contains
Pontecorvo–Maki–Nakagawa–Sakata matrix
Pontecorvo–Maki–Nakagawa–Sakata_matrix
all linear forms on a given vector space. elementary matrix Square matrix that differs from the identity matrix by at most one entry hyperbolic unit 1. An
Glossary_of_linear_algebra
Concept in linear algebra
Householder transformation (also known as a Householder reflection or elementary reflector) is a linear transformation that describes a reflection about
Householder_transformation
On the number of spanning trees in a graph
Laplacian matrix L of G is the difference between the graph's degree matrix (the diagonal matrix of vertex degrees) and its adjacency matrix (a (0,1)-matrix with
Kirchhoff's_theorem
Function of the coefficients of a polynomial that gives information on its roots
for any symmetric matrix A, there is an elementary matrix S such that S T A S {\displaystyle S^{\mathrm {T} }A\,S} is a diagonal matrix. Then the discriminant
Discriminant
Algorithmic runtime requirements for common math procedures
Many of the methods in this section are given in Borwein & Borwein. The elementary functions are constructed by composing arithmetic operations, the exponential
Computational complexity of mathematical operations
Computational_complexity_of_mathematical_operations
Precursor physical model to string theory and quantum chromodynamics
S-matrix theory was a proposal for replacing local quantum field theory as the basic principle of elementary particle physics. It avoided the notion of
S-matrix_theory
American mathematician and educator (1914–1979)
Mathematical Thought (1957) Introduction to Linear Algebra (1959) Elementary Matrix Algebra (1969) Algebraic Structures (1974) While discrimination against
Marjorie_Lee_Browne
Mathematical concept
In mathematics, a symplectic matrix is a 2 n × 2 n {\displaystyle 2n\times 2n} matrix M {\displaystyle M} with real entries that satisfies the condition
Symplectic_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
Permutation_matrix
Mathematical technique
square matrices and I is the identity matrix. Given the polynomial p, the matrices A and B can be found by elementary methods. The polynomial x2 + y2 is
Matrix factorization of a polynomial
Matrix_factorization_of_a_polynomial
Concepts from linear algebra
the matrix multiplication A v = λ v , {\displaystyle A\mathbf {v} =\lambda \mathbf {v} ,} where the eigenvector v is an n × 1 matrix. For a matrix, eigenvalues
Eigenvalues_and_eigenvectors
be viewed as a sequence of applying left matrix multiplication using elementary row operations using elementary matrices ( E n {\displaystyle \mathbf {E}
Methods_of_matrix_inversion
Elementary particle, fundamental constituent of matter
A quark (/ˈkwɔːrk, ˈkwɑːrk/ ) is a type of elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called
Quark
American actor (born 1943)
film audiences, he is best known for his portrayal of the Keymaker in The Matrix franchise, and as the voice of Master Oogway in the Kung Fu Panda franchise
Randall_Duk_Kim
Matrix consisting of a single row or column
m\times 1} matrix consisting of a single column of m {\displaystyle m} entries. Similarly, a row vector is a 1 × n {\displaystyle 1\times n} matrix, consisting
Row_and_column_vectors
Mathematical equivalence relation
{\displaystyle B=Q^{-1}AP} for some invertible n-by-n matrix P and some invertible m-by-m matrix Q. Equivalent matrices represent the same linear transformation
Matrix_equivalence
matrices which differ from the identity matrix in only a finite number of coefficients. An elementary matrix here is a transvection: one such that all
Whitehead_torsion
Algebraic structure
Springer, p. 250, ISBN 9783540737247. Eves, Howard Whitley (1980), Elementary Matrix Theory, Dover, p. 183, ISBN 9780486150277. Herstein 1975, pp. 155
Polynomial_ring
Polynomial whose roots are the eigenvalues of a matrix
algebra, the characteristic polynomial of a square matrix is a polynomial which is invariant under matrix similarity and has the eigenvalues as roots. It
Characteristic_polynomial
Matrix decomposition
complex matrix into a rotation, followed by a scaling, followed by another rotation. It generalizes the eigendecomposition of a square normal matrix with
Singular_value_decomposition
Vector satisfying some of the criteria of an eigenvector
algebra, a generalized eigenvector of an n × n {\displaystyle n\times n} matrix A {\displaystyle A} is a vector which satisfies certain criteria which are
Generalized_eigenvector
Mathematical function
value of en. Thus the determinant of a square matrix is the product of the eigenvalues. The set of elementary symmetric polynomials in n variables generates
Elementary symmetric polynomial
Elementary_symmetric_polynomial
Several equations of degree 1 to be solved simultaneously
of redirect targets Matrix decomposition – Representation of a matrix as a product Matrix splitting – Representation of a matrix as a sum NAG Numerical
System_of_linear_equations
Family of linear error-correcting codes
permutations (swapping columns) Elementary row operations (replacing a row with a linear combination of rows) Example From the above matrix we have 2k = 24 = 16
Hamming_code
Theory in particle physics
or hadron boostrap is a superseded hypothesis about the composition of elementary particles interacting under the strong nuclear interaction. It uses general
Bootstrap_model
Practical mathematics used in business
includes elementary arithmetic, elementary algebra, statistics and probability. For some management problems, more advanced mathematics - calculus, matrix algebra
Business_mathematics
Subject area in mathematics
Define an elementary matrix to be one which is the sum of an identity matrix and a single off-diagonal element (this is a subset of the elementary matrices
Algebraic_K-theory
Function's sensitivity to argument change
many different directions, and is thus computed from the geometry of the matrix. More generally, condition numbers can be defined for non-linear functions
Condition_number
American mathematician (1911–2004)
a Complex Variable, v. 1, Boston: Prindle, Weber & Schmidt 1966. Elementary matrix theory, Boston: Allyn and Bacon [Reprint: 1980. Dover Publications
Howard_Eves
A matrix canonical form
linear algebra, a Weyr canonical form (or, Weyr form or Weyr matrix) is a square matrix which (in some sense) induces "nice" properties with matrices
Weyr_canonical_form
Theorem in linear algebra
In matrix theory, the Perron–Frobenius theorem, proved in its first part by Oskar Perron (1907) and extended by Georg Frobenius (1912), asserts that a
Perron–Frobenius_theorem
Vectors mapped to 0 by a linear map
kernel of a matrix may be computed by Gaussian elimination. For this purpose, given an m × n matrix A, we construct first the row augmented matrix [ A I ]
Kernel_(linear_algebra)
Storage method in computer memory
matrix is equal to the number of rows of the second matrix. Hence, if an m × n matrix is multiplied with an n × r matrix, then the resultant matrix will
Matrix_representation
Matrix normal form
the matrix A {\displaystyle A} . The elements α i {\displaystyle \alpha _{i}} are unique up to multiplication by a unit and are called the elementary divisors
Smith_normal_form
Improved reduction for specific matrices
In numerical linear algebra, the tridiagonal matrix algorithm, also known as the Thomas algorithm (named after Llewellyn Thomas), is a simplified form
Tridiagonal_matrix_algorithm
Square matrices satisfy their characteristic equation
mathematicians Arthur Cayley and William Rowan Hamilton) states that every square matrix over a commutative ring (such as the real or complex numbers or the integers)
Cayley–Hamilton_theorem
Notions of sums for matrices in linear algebra
1&3\\-6&-5\\-1&1\end{bmatrix}}} Matrix multiplication Vector addition Direct sum of matrices Kronecker sum Elementary Linear Algebra by Rorres Anton 10e
Matrix_addition
Concept in mathematics
(1922), "On the determinant of an hermitian matrix with quaternionic elements. Definition and elementary properties with applications." (PDF), Bulletin
Moore determinant of a Hermitian matrix
Moore_determinant_of_a_Hermitian_matrix
Standard representation of a mathematical object
matrix similarity. The row echelon form is a canonical form, when one considers as equivalent a matrix and its left product by an invertible matrix.
Canonical_form
Irreducible representation of the rotation group SO
The Wigner D-matrix is a unitary matrix in an irreducible representation of the groups SU(2) and SO(3). It was introduced in 1927 by Eugene Wigner, and
Wigner_D-matrix
Species of elementary particle
In particle physics, flavour or flavor refers to the species of an elementary particle. The Standard Model counts six flavours of quarks and six flavours
Flavour_(particle_physics)
Function approximating net physical effect
underlying physics, but instead, providing the momentum dependence of suitable matrix elements. It is further measured experimentally in confirmation or specification
Form factor (quantum field theory)
Form_factor_(quantum_field_theory)
Geometric transformation that preserves lines but not angles nor the origin
transformation is invertible, the square matrix A {\displaystyle A} appearing in its matrix representation is invertible. The matrix representation of the inverse
Affine_transformation
Coordinate change in linear algebra
A {\displaystyle A} is the change-of-basis matrix (also called transition matrix), which is the matrix whose columns are the coordinates of the "new"
Change_of_basis
British mathematician (1826–1883)
remembered for his work in elementary divisors, quadratic forms, and Smith–Minkowski–Siegel mass formula in number theory. In matrix theory he is visible today
Henry_John_Stephen_Smith
Random process independent of past history
identity matrix of size n, and 0n,n is the zero matrix of size n×n. Multiplying together stochastic matrices always yields another stochastic matrix, so Q
Markov_chain
Algorithm for determinants of integers
follows that, for an n × n matrix of maximum (absolute) value 2L for each entry, the Bareiss algorithm runs in O(n3) elementary operations with an O(nn/2 2nL)
Bareiss_algorithm
Unified description of electromagnetism and the weak interaction
to the unification of the weak and electromagnetic interaction between elementary particles, known as the Weinberg–Salam theory. The existence of the electroweak
Electroweak_interaction
Type of matrix representation
complex matrix A {\displaystyle A} is a factorization of the form A = U P {\displaystyle A=UP} , where U {\displaystyle U} is a unitary matrix, and P {\displaystyle
Polar_decomposition
inertia additivity formula Matrix equivalence Matrix congruence Matrix similarity Matrix consimilarity Row equivalence Elementary row operations Householder
Outline_of_linear_algebra
ELEMENTARY MATRIX
ELEMENTARY MATRIX
ELEMENTARY MATRIX
ELEMENTARY MATRIX
Boy/Male
Indian
The judge
Girl/Female
Tamil
Nishkaina | நீஷà¯à®•à¯ˆà®¨à®¾
Selfless
Girl/Female
Bengali, Gujarati, Hindu, Indian, Jain, Kannada, Malayalam, Marathi, Oriya, Sindhi, Telugu
Fame; Reputation; Popularity; Famous
Boy/Male
Hindu
Palace, One of the three worlds
Boy/Male
Tamil
Noble, Wise, Faultless, Transparent
Girl/Female
Indian, Tamil
Loveable
Boy/Male
Sikh
God of grandeur
Girl/Female
British, English
Form of Dominick; Belonging to God
Biblical
given or offered
Surname or Lastname
English
English : nickname from Middle English child ‘child’, ‘infant’ (Old English cild), in various possible applications. The word is found in Old English as a byname, and in Middle English as a widely used affectionate term of address. It was also used as a term of status for a young man of noble birth, although the exact meaning is not clear; in the 13th and 14th centuries it was a technical term used of a young noble awaiting elevation to the knighthood. In other cases it may have been applied as a byname to a youth considerably younger than his brothers or to one who was a minor on the death of his father.English : possibly a topographic name from Old English cielde ‘spring (water)’, a rare word derived from c(e)ald ‘cold’.
ELEMENTARY MATRIX
ELEMENTARY MATRIX
ELEMENTARY MATRIX
ELEMENTARY MATRIX
ELEMENTARY MATRIX
a.
Relating to hypostasis, or substance; hence, constitutive, or elementary.
a.
Pertaining to aliment or food, or to the function of nutrition; nutritious; alimental; as, alimentary substances.
a.
Elementary.
n.
The doctrine of the elementary requisites of mere thought.
a.
Regulative.
n.
Unorganized material; elementary matter.
a.
Having only one principle or constituent part; consisting of a single element; simple; uncompounded; as, an elementary substance.
a.
Pertaining to rudiments or first principles; rudimentary; elementary.
n.
The whole alimentary, or enteric, canal.
a.
Pertaining to, or treating of, the elements, rudiments, or first principles of anything; initial; rudimental; introductory; as, an elementary treatise.
a.
Pertaining to one of the four elements, air, water, earth, fire.
a.
Elementary.
a.
Elementary; rudimental.
a.
Combined with arsenic; -- said some elementary substances or radicals; as, arseniureted hydrogen.
n.
The state of being elementary; original simplicity; uncompounded state.
a.
Capable of being leased; held by tenants.
n.
Elementariness.
n.
An elementary piece of the mechanism of a lock.
a.
Pertaining to the elements, first principles, and primary ingredients, or to the four supposed elements of the material world; as, elemental air.
adv.
According to elements; literally; as, the words, "Take, eat; this is my body," elementally understood.