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Square matrix with ones on a superdiagonal or subdiagonal
mathematics, a shift matrix is a binary matrix with ones only on the superdiagonal or subdiagonal, and zeroes elsewhere. A shift matrix U with ones on
Shift_matrix
Families of matrices in mathematics, physics, and quantum information
physics. The clock matrix amounts to the exponential of position in a "clock" of d {\displaystyle d} hours, and the shift matrix is just the translation
Generalizations of Pauli matrices
Generalizations_of_Pauli_matrices
Topics referred to by the same term
§ Sequences, a linear operator in functional analysis Shift matrix, the finite-dimensional analogue Right Shift key, a key on a computer keyboard Rightshifting
Right_shift
Topics referred to by the same term
computer operation Shift operator § Sequences, a linear operator in functional analysis Shift matrix, the finite-dimensional analogue Left Shift key, a key on
Left_shift
Square matrix constructed from a monic polynomial
roots of unity, the companion matrix and its transpose both reduce to Sylvester's cyclic shift matrix, a circulant matrix. Consider a polynomial p ( x
Companion_matrix
Mathematical concept in algebra
In linear algebra, a nilpotent matrix is a square matrix N such that N k = 0 {\displaystyle N^{k}=0\,} for some positive integer k {\displaystyle k}
Nilpotent_matrix
American media franchise
The Matrix is an American cyberpunk media franchise consisting of four feature films, beginning with The Matrix (1999) and continuing with three sequels
The_Matrix_(franchise)
Key on typewriter or computer keyboard
am PC? Wo ist die Shift-Taste?". GEEKOM (in German). 2024-08-19. Retrieved 2026-07-05. Dribin, Dave (2000-06-24). "Keyboard Matrix Help". www.dribin.org
Shift_key
Unit of digital information, usually 8 bits
2020. octet An eight bit byte. Buchholz, Werner (1956-06-11). "7. The Shift Matrix" (PDF). The Link System. IBM. pp. 5–6. Stretch Memo No. 39G. Archived
Byte
2021 film by Lana Wachowski
The Matrix Resurrections is a 2021 American science fiction action film co-produced and directed by Lana Wachowski, who co-wrote the screenplay with David
The_Matrix_Resurrections
Multichannel audio technology
{\displaystyle j=+90^{\circ }} phase-shift, k = − 90 ∘ {\displaystyle k=-90^{\circ }} phase-shift The basic SQ matrix had mono/stereo anomalies as well as
Matrix_decoder
Planar movement within a Euclidean space without rotation
interpreted as the addition of a constant vector to every point, or as shifting the origin of the coordinate system. In a Euclidean space, any translation
Translation_(geometry)
Square matrix of cyclically shifted rows
In linear algebra, a circulant matrix is a square matrix in which each row is a cyclic shift, by one position, of the row above it. Equivalently, its
Circulant_matrix
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
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
Norm on a vector space of matrices
Consider the matrix as a rectangular array of numbers; then a matrix norm may be defined as a function of the entries of the matrix. Such matrix norms are
Matrix_norm
Unit of information
June 2016 at the Wayback Machine Buchholz, Werner (1956-06-11). "7. The Shift Matrix" (PDF). The Link System. IBM. pp. 5–6. Stretch Memo No. 39G. Archived
Bit
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
Infinite matrices with Pascal's triangle as elements
In matrix theory and combinatorics, a Pascal matrix is a matrix (possibly infinite) containing the binomial coefficients as its elements. It is thus an
Pascal_matrix
projection matrix P, defined as a matrix such that P2 = P, has index 1 (or 0) and has Drazin inverse PD = P. If A is a nilpotent matrix (for example a shift matrix)
Drazin_inverse
Risk assessment comparing the likelihood of a risk to its severity
A risk matrix is a matrix that is used during risk assessment to define the level of risk by considering the category of likelihood (often confused with
Risk_matrix
Operator on a Hilbert space that shifts basis vectors
infinite-dimensional lower shift matrix. The adjoint of the unilateral shift, denoted S ∗ {\displaystyle S^{*}} , is the backward shift. It acts on ℓ 2 {\displaystyle
Unilateral_shift_operator
name for many reasons. […] Buchholz, Werner (11 June 1956). "7. The Shift Matrix" (PDF). The Link System. IBM. pp. 5–6. Stretch Memo No. 39G. Archived
List of computer term etymologies
List_of_computer_term_etymologies
German-American computer scientist (1922–2019)
spelling variant in German). Buchholz, Werner (1956-06-11). "7. The Shift Matrix". The Link System (PDF). IBM. pp. 5–6. Stretch Memo No. 39G. Archived
Werner_Buchholz
Compact station wagon by Toyota, 2002–2014
The Toyota Matrix, officially named Toyota Corolla Matrix, is a compact hatchback manufactured by Toyota Motor Manufacturing Canada in Cambridge, Ontario
Toyota_Matrix
Kind of square matrix in linear algebra
Hessenberg matrix can be further reduced to a triangular matrix through Shifted QR-factorization combined with deflation steps. Reducing a general matrix to a
Hessenberg_matrix
Matrix with non-zero elements only in a diagonal band
In mathematics, particularly matrix theory, a band matrix or banded matrix is a sparse matrix whose non-zero entries are confined to a diagonal band, comprising
Band_matrix
Matrix decomposition
(also known as eigenvalue decomposition or EVD) is a factorization of a matrix A {\displaystyle A} into a canonical form given by A = Q D Q − 1 {\displaystyle
Eigendecomposition of a matrix
Eigendecomposition_of_a_matrix
Type of beamforming network
{\displaystyle n\times n} matrix ( n {\displaystyle n} some power of two) with hybrid couplers and fixed-value phase shifters at the junctions. The device
Butler_matrix
Numerical methods for matrix eigenvalue calculation
finding the eigenvalues of a matrix. These eigenvalue algorithms may also find eigenvectors. Given an n × n square matrix A of real or complex numbers
Eigenvalue_algorithm
Last human city in The Matrix film series
a contrast to the Matrix, "The racial constituency of Zion is much less European and Anglo than present-day America. We are shifting the paradigm from
Zion_(The_Matrix)
Display that uses the light-modulating properties of liquid crystals
environmental concerns, manufacturers shifted to black colored photoresist with carbon pigment as the black matrix material. Another color-generation method
Liquid-crystal_display
Matrix with shifting rows
In linear algebra, a Toeplitz matrix or diagonal-constant matrix, named after Otto Toeplitz, is a matrix in which each descending diagonal from left to
Toeplitz_matrix
Series of analog synthesizers
Oberheim Matrix synthesizers were a product line of subtractive analog synthesizers from Oberheim featuring a system of modulation which Oberheim called
Oberheim_Matrix_synthesizers
Metaphor for a choice of truth or illusion
from the Matrix. In a 2012 interview, Matrix director Lana Wachowski said: What we were trying to achieve with the story overall was a shift, the same
Red_pill_and_blue_pill
The Knight shift is a shift in the nuclear magnetic resonance (NMR) frequency of a paramagnetic substance first published in 1949 by the UC Berkeley physicist
Knight_shift
Boston Consulting Group business analysis method
The growth–share matrix (also known as the product portfolio matrix, Boston Box, BCG-matrix, Boston matrix, Boston Consulting Group portfolio analysis
Growth–share_matrix
Motor vehicle transmission
synchromesh for the shift from third gear to second gear (drivers' manuals in vehicles suggested that if the driver needed to shift from second to first
Manual_transmission
Sum of elements on the main diagonal
In linear algebra, the trace of a square matrix A, denoted tr(A), is defined as a sum of the elements on its main diagonal, a 11 + a 22 + ⋯ + a n n {\displaystyle
Trace_(linear_algebra)
College football rating system
polls, one being Colley Matrix, to determine the host site for its conference championship game in football, due to "a shift to place a priority on head-to-head
Colley_Matrix
Algorithm to calculate eigenvalues
Hessenberg matrix A {\displaystyle A} are: Pick a shift μ {\displaystyle \mu } and subtract it from all diagonal elements, producing the matrix A − μ I {\displaystyle
QR_algorithm
Fee schedule for District of Columbia lawyers
attorneys' fee awards under federal fee-shifting statutes. Look up matrix in Wiktionary, the free dictionary. The Laffey Matrix originated in Laffey v. Northwest
Laffey_Matrix
Form of a matrix indicating its eigenvalues and their algebraic multiplicities
_{n}{\color {red}\lrcorner }\\\end{array}}\right]} Example of a matrix in Jordan normal form. All matrix entries not shown are zero. The outlined squares are known
Jordan_normal_form
Algorithms for matrix decomposition
Non-negative matrix factorization (NMF or NNMF), also non-negative matrix approximation is a group of algorithms in multivariate analysis and linear algebra
Non-negative matrix factorization
Non-negative_matrix_factorization
Optical device which splits a beam of light in two
will have a phase shift of π, while the transmitted wave will not have a phase shift; the blue arrow does not pick up a phase-shift, because it is reflected
Beam_splitter
Type of shift space studied in ergodic theory
the case of the two-sided shift. A particularly useful subclass is given by the edge shifts. Let A be an n × n adjacency matrix with entries in {0, 1}.
Subshift_of_finite_type
Method of encoding digital data on multiple carrier frequencies
matrix with some diagonal phase shift matrices. Then, the right hand side DFT/IDFT matrix and the k {\displaystyle k} th diagonal phase shift matrix in
Orthogonal frequency-division multiplexing
Orthogonal_frequency-division_multiplexing
Analogue synthesizer
keyboardless, six-voice version of the Matrix-12 (released a year later, in 1985). Utilizing Oberheim's Matrix Modulation technology, the Xpander combined
Oberheim_Xpander
Matrix 4-channel quadraphonic sound system
Matrix H was developed by BBC engineers in the late 1970s to carry quadraphonic sound via FM radio in a way that would be most compatible with existing
Matrix_H
Device to determine relative phase shift
/ 2 {\displaystyle i/{\sqrt {2}}} . The phase shifter on the upper arm is modelled as the unitary matrix P = ( 1 0 0 e i Δ Φ ) {\displaystyle
Mach–Zehnder_interferometer
Concepts from linear algebra
cyclic permutation matrix A = [ 0 1 0 0 0 1 1 0 0 ] . {\displaystyle A={\begin{bmatrix}0&1&0\\0&0&1\\1&0&0\end{bmatrix}}.} This matrix shifts the coordinates
Eigenvalues_and_eigenvectors
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)
Linear operator
characteristic polynomials for the principal submatrices of the shift operator. Hankel matrix Meurant, Gérard; Sommariva, Alvise (2014). "Fast variants of
Jacobi_operator
Spectral line splitting in electrical field
D-matrix. The first-order perturbation matrix on basis of the unperturbed rigid rotor function is non-zero and can be diagonalized. This gives shifts and
Stark_effect
Typographic symbol
"the determinant of the matrix A". When the matrix entries are written out, the determinant is denoted by surrounding the matrix entries by vertical bars
Vertical_bar
Formulation of quantum mechanics
Matrix mechanics is a formulation of quantum mechanics created by Werner Heisenberg, Max Born, and Pascual Jordan in 1925. It was the first conceptually
Matrix_mechanics
Class of pseudorandom number generators
However, it fails the MatrixRank and LinearComp tests of the BigCrush test suite from the TestU01 framework. All use three shifts and three or four exclusive-or
Xorshift
1995 book by Bracha L. Ettinger
the matrix is a metaphorical reference to the uterus (matrix - womb) in order to discuss the origins of human ethics and relationality. This shift was
The_Matrixial_Gaze
Matrix 4-channel quadraphonic sound system developed by Sansui Electric
Synthesizer, and later incorrectly referred to as RM or Regular Matrix) was a phase amplitude matrix 4-channel quadraphonic sound system for phonograph records
QS_Regular_Matrix
Notion in statistics
some initial results by Francis Ysidro Edgeworth). The Fisher information matrix is used to calculate the covariance matrices associated with maximum-likelihood
Fisher_information
Type of shift register in computing
In computing, a linear-feedback shift register (LFSR) is a shift register whose input bit is a linear function of its previous state. The most commonly
Linear-feedback shift register
Linear-feedback_shift_register
name for many reasons. [...] Buchholz, Werner (June 11, 1956). "7. The Shift Matrix" (PDF). The Link System. IBM. pp. 5–6. Stretch Memo No. 39G. Archived
Timeline_of_binary_prefixes
Display technology for use in mobile devices and televisions
Active-matrix organic light-emitting diode (AMOLED) screens are a type of OLED display device technology. OLED describes a specific type of thin-film-display
AMOLED
Function in discrete mathematics
expression can also be written in terms of a DFT matrix. When scaled appropriately, it becomes a unitary matrix, and the DFT can thus be viewed as a transformation
Discrete_Fourier_transform
Transforms equations for numerical solution
system matrix ( A − λ ~ ⋆ I ) {\displaystyle (A-{\tilde {\lambda }}_{\star }I)} , which becomes as expensive for large problems as the shift-and-invert
Preconditioner
Block diagonal matrix of Jordan blocks
the mathematical discipline of matrix theory, a Jordan matrix, named after Camille Jordan, is a block diagonal matrix over a ring R (whose identities
Jordan_matrix
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
Ability of a computer keyboard to correctly handle several simultaneous keystrokes
shift keys by default. Computer keyboards typically are designed to detect these keys being activated in addition to others from the character matrix
Key_rollover
American stuntman and film director
and coordinator, notably as the key stunt double for Keanu Reeves on The Matrix (1999), and as the martial arts stunt coordinator on its first two sequels
Chad_Stahelski
Iterative method for solving the Sylvester matrix equations
iterative method used to solve Sylvester matrix equations. It is a popular method for solving the large matrix equations that arise in systems theory and
Alternating-direction implicit method
Alternating-direction_implicit_method
Discrete fourier transform expressed as a matrix
applied mathematics, a DFT matrix is a square matrix as an expression of a discrete Fourier transform (DFT) as a transformation matrix, which can be applied
DFT_matrix
Surjective bounded operator on a Hilbert space preserving the inner product
bilateral shift on the sequence space ℓ2 indexed by the integers is unitary. The unilateral shift (right shift) is an isometry; its conjugate (left shift) is
Unitary_operator
Matrix-valued random variable
probability theory and mathematical physics, a random matrix is a matrix-valued random variable—that is, a matrix in which some or all of its entries are sampled
Random_matrix
Concept in physics
therefore shifted and overlapping. Figure 1 shows the typical line shape for electronic transitions of individual chromophores in a solid matrix. The zero-phonon
Zero-phonon line and phonon sideband
Zero-phonon_line_and_phonon_sideband
N x N matrix describing a linear power system with N buses
In power engineering, nodal admittance matrix (or just admittance matrix) is an N x N matrix describing a linear power system with N buses. It represents
Nodal_admittance_matrix
Canadian animated TV series
the adventures of a Guardian named Bob and his companions Enzo and Dot Matrix within the computer system world of Mainframe as they work to keep it safe
ReBoot
Ecological concept
N_{e}=N+{\begin{matrix}{\frac {1}{2}}\end{matrix}}} or more generally, N e = N + D 2 {\displaystyle N_{e}=N+{\begin{matrix}{\frac {D}{2}}\end{matrix}}} where
Effective_population_size
Metropolitan Reticular Matrix (1996) planning
Metropolitan Reticular Matrix Planning (also known as 'CT' planning - see below) is an approach to managing the growth of metropolises. It is a type of
Metropolitan Reticular Matrix Planning
Metropolitan_Reticular_Matrix_Planning
Topics referred to by the same term
whose Schläfli matrix has only positive eigenvalues Coxeter matrix of finite type, a Coxeter matrix whose associated Schläfli matrix has only positive
Finite_type
Type of matrix barcode
DotCode is a two-dimensional (2D) matrix barcode invented in 2008 by Hand Held Products as a replacement for the outdated Code 128. At this time, it is
DotCode
Hot metal typesetting machine (1886–1980s)
particular size. The letter forms are engraved into one side of the matrix. The most common matrix has two letter forms on it, the normal and auxiliary positions
Linotype_machine
Variant of a liquid-crystal display
as addressability and contrast. A TFT LCD is an active matrix LCD, in contrast to passive matrix LCDs or simple, direct-driven (i.e. with segments directly
TFT_LCD
Soft carbonated drink
had shifted toward locally produced alternatives, while 72% believed the boycotts did not negatively affect the Jordanian national economy. Matrix's marketing
Matrix_Carbonated_Drink
fierce appearance." Coptoborus trinity Smith & Cognato, 2021 Trinity, The Matrix "Three types of setae (trifid, scale-like and bristle-like) help diagnose
List of organisms named after works of fiction
List_of_organisms_named_after_works_of_fiction
Changing between languages during a conversation
linguistics, code-switching or language alternation is the process of shifting from one linguistic code (a language or dialect) to another, depending
Code-switching
Used for the resultant of two polynomials
In mathematics, a Sylvester matrix is a matrix associated to two univariate polynomials that have coefficients in a commutative ring (such as an integral
Sylvester_matrix
Type of large language model
Hierarchical k-means Fuzzy Expectation–maximization (EM) DBSCAN OPTICS Mean shift Dimensionality reduction Factor analysis Exploratory CCA ICA LDA NMF PCA
Generative pre-trained transformer
Generative_pre-trained_transformer
British engineer
J. N.; Chiang, R. Y. (1989). "Simplifying the H∞ theory via loop-shifting, matrix-pencil and descriptor concepts". International Journal of Control.
David_Limebeer
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
American biotechnology company
patient-centered medical decision making.[citation needed] In 2012 CombiMatrix shifted its focus from providing oncology genetic testing to developmental testing
Invitae
Approximation method in statistics
identity matrix. Increasing the value of λ {\displaystyle \lambda } has the effect of changing both the direction and the length of the shift vector. The
Non-linear_least_squares
Matrix 4-channel quadraphonic sound system
Benjamin Bauer. His basic formula used 90 degree phase shift circuitry to enable enhanced 4-2-4 matrix systems to be developed. This 4-2-4 process could not
Stereo_Quadraphonic
industry. The Private Market Assets Matrix (PMAM), also called Infrastructure and Private Markets Investment Matrix, is an original strategic assessment
Private_market_assets
Material made from a combination of two or more unlike substances
resin or thermoplastics as a binder Ceramic matrix composites (composite ceramic and metal matrices) Metal matrix composites Advanced composite materials
Composite_material
Sociological paradigm
The matrix of domination or matrix of oppression is a sociological paradigm that explains issues of oppression that deal with race, class, and gender,
Matrix_of_domination
Scalar measure of the rotational inertia with respect to a fixed axis of rotation
inertia matrix is a constant real symmetric matrix. A real symmetric matrix has the eigendecomposition into the product of a rotation matrix Q {\displaystyle
Moment_of_inertia
challenges Dan to a battle which he reluctantly accepts. The scene then shifts to the beginning of the "Great Collision" from 12 years ago. Dan Kouzo and
List of Bakugan: Battle Planet episodes
List_of_Bakugan:_Battle_Planet_episodes
Arithmetic notation system
{\displaystyle {\begin{matrix}&\underbrace {a_{}^{a^{{}^{.\,^{.\,^{.\,^{a}}}}}}} &\\&b{\mbox{ copies of }}a\end{matrix}}} Cutler's bar notation shifts these exponentials
Cutler's_bar_notation
Diode that emits light from an organic compound
different mode of operation. An OLED display matrix can have various control schemes: A passive-matrix (PMOLED) where each row and line in the display
OLED
Basic circuit in quantum computing
sphere by φ {\displaystyle \varphi } radians. The phase shift gate is represented by the matrix: P ( φ ) = [ 1 0 0 e i φ ] {\displaystyle P(\varphi
Quantum_logic_gate
travel, tourism, insurance
SHIFT MATRIX
SHIFT MATRIX
SHIFT MATRIX
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SHIFT MATRIX
SHIFT MATRIX
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