matrix

Definitions

  • WordNet 3.6
    • n matrix mold used in the production of phonograph records, type, or other relief surface
    • n matrix the formative tissue at the base of a nail
    • n matrix the body substance in which tissue cells are embedded
    • n matrix (mathematics) a rectangular array of quantities or expressions set out by rows and columns; treated as a single element and manipulated according to rules
    • n matrix an enclosure within which something originates or develops (from the Latin for womb)
    • n matrix (geology) amass of fine-grained rock in which fossils, crystals, or gems are embedded
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Webster's Revised Unabridged Dictionary
  • Interesting fact: In the movie "The Matrix Reloaded" a 17 minute battle scene cost over $40 million to produce
    • matrix (Math) A rectangular arrangement of symbols in rows and columns. The symbols may express quantities or operations.
    • matrix That which gives form or origin to anything
    • matrix The cavity in which anything is formed, and which gives it shape; a die; a mold, as for the face of a type.
    • matrix The earthy or stony substance in which metallic ores or crystallized minerals are found; the gangue.
    • matrix The five simple colors, black, white, blue, red, and yellow, of which all the rest are composed.
    • matrix (Biol) The lifeless portion of tissue, either animal or vegetable, situated between the cells; the intercellular substance.
    • matrix (Anat) The womb. "Before I formed thee in the belly I knew thee.""All that openeth the matrix is mine."
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Century Dictionary and Cyclopedia
    • n matrix The womb; the uterus.
    • n matrix Hence That which incloses anything, or gives origin to anything, like a womb. A mold which gives form to material forced into it in a solid condition, or poured into it in a fluid state and allowed to harden before removal.
    • n matrix In mathematics, a rectangular array of quantities, usually square: so called because considered as a mold or set of compartments into which a certain number of quantities can be put, the leaving of one of the spaces unoccupied being in effect to put zero there. : The matrix is consequently a multiple quantity having as many dimensions as it has spaces. The numbers in the spaces are called the constituents of the matrix. The following definitions relate to square matrices. The vertical lines of numbers are called the columns, the horizontal ones the rows. The diagonal running from the upper left hand to the lower right hand corner is called the principal diagonal. Constituents symmetrically situated with reference to the principal diagonal are said to be conjugate. A matrix in which every constituent is equal to its conjugate is said to be symmetrical; if all the constituents along each diagonal band transverse to the principal diagonal are equal, the matrix is said to be persymmetrical. The addition of matrices is so understood that the sum of two like matrices is a matrix every constituent of which is equal to the sum of the corresponding constituents of the parts. The multiplication of two like square matrices is so understood that the product is a matrix whose construction is of the kind shown in the following example
    • n matrix a matrix with p columns and q rows. The types of two matrices are said to be complementary when p—p = q + q.
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Chambers's Twentieth Century Dictionary
    • n Matrix mā′triks or mat′riks (anat.) the cavity in which an animal is formed before its birth, the womb: the cavity in which anything is formed, a mould: : :
    • n Matrix mā′triks or mat′riks (mining) earthy or stony substances in which minerals are found embedded
    • n Matrix mā′triks or mat′riks (dyeing) the five simple colours (black, white, blue, red, and yellow) from which all the others are formed
    • n Matrix mā′triks or mat′riks (math.) a rectangular array of quantities, usually square—a multiple quantity having as many dimensions as it has spaces
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Etymology

Webster's Revised Unabridged Dictionary
L., fr. mater, mother. See Mother, and cf. Matrice
Chambers's Twentieth Century Dictionary
L. matrix, -icismater, mother.

Usage

In literature:

The unity of the world has nothing to do with any 'matrix.
"The Will to Believe" by William James
Matrix of monastic seal, 263.
"Notes and Queries, Index of Volume 3, January-June, 1851" by Various
The Central Directory Matrix is here.
"Starman's Quest" by Robert Silverberg
Older zoogloeae may precipitate oxide of iron in the matrix, if that metal exists in small quantities in the medium.
"Encyclopaedia Britannica, 11th Edition, Volume 3, Part 1, Slice 2" by Various
In limestone much of the mass may be replaced by garnet and other silicates in a matrix of quartz.
"The Economic Aspect of Geology" by C. K. Leith
To find any fault with the matrix of this opal is probably blasphemous.
"A History of the French Novel, Vol. 2" by George Saintsbury
Here galleries branch out in various directions, hewn in the slate forming the matrix of the vein.
"The Mines and its Wonders" by W.H.G. Kingston
Resupinate, attached to the matrix by the back.
"The Mushroom, Edible and Otherwise" by M. E. Hard
It consists of a strong, hard material imbedded in a matrix of softer material.
"Thin Edge" by Gordon Randall Garrett
Probably it originated in the matrix of nations which the table-land of Asia was.
"The Lords of the Ghostland" by Edgar Saltus
Although no experiments were carried out, Nikolaiewa asserts that this organism forms the matrix of the grains.
"The Bacillus of Long Life" by Loudon Douglas
The gems are found in a matrix of black slate in what appears to be the crater of a volcano, and are mined in a very crude manner.
"Encyclopaedia Britannica, 11th Edition, Volume 6, Slice 6" by Various
With a fact for matrix it developed as rapidly as a spark mounts into flame.
"Eden" by Edgar Saltus
The matrix most commonly used is Portland cement, by far the best and strongest of them all.
"Encyclopaedia Britannica, 11th Edition, Volume 6, Slice 7" by Various
The Disraeli-matrix swept on into oratorical periods that made the walls ring.
"The Ego Machine" by Henry Kuttner
The Possible is a terrible matrix.
"Toilers of the Sea" by Victor Hugo
The drama of the future was shaping in a matrix which was the best possible to assure a long life, under popular, natural conditions.
"How to See a Play" by Richard Burton
Let us suppose, Fred mused, that deep within the mind there is some matrix of thought that ties the human to this universe.
"Ye of Little Faith" by Roger Phillips Graham
It was a warm April day when they set out, with a sky like the matrix of turquoise.
"Carnival" by Compton Mackenzie
If a simple mineral or shell, in place of being detached, be still fixed in a portion of rock, it is said to be in its matrix.
"Principles of Geology" by Charles Lyell
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In poetry:

That through the clouded matrix saw
The crystal planes of shaping law,
Through these the sovereign skill that planned,--
The Father's care, the Master's hand!
"Benjamin Peirce" by Oliver Wendell Holmes

In news:

AMX has released the AutoPatch Epica Digital Generation (EpicaDG) line of fiber optic matrix switchers , which are designed for large AV installations in command & control applications.
Since traditional matrix switchers cannot handle HD video, the V2070 lets operators have a fully functional HD control room solution with HD (1080P/720P) video inputs and 16 HD video outputs.
Intelix's DIGI-HD-8X8 matrix switcher .
Slo-Mo Stupefaction From 'Matrix' Creators.
TriReme Receives FDA Approval for Expanded Matrix of Novel Glider PTCA Balloon Catheter.
TriReme Medical Inc (TMI) announced that it has received US Food and Drug Administration (FDA) clearance for an expanded matrix of sizes for its unique Glider percutaneous transluminal coronary angioplasty (PTCA) balloon catheter.
Products Finishing, Arthur S. Can one apply electroless nickel over a tungsten metal matrix.
Confidex has been ranked at the top of the latest Vendor Matrix released by ABI Research.
Remember when "The Matrix" came out in 1999 and its disciples treated it like a philosophy textbook.
One of Toyota's Geneva debuts is the redesigned Verso , Europe's bigger version of the Matrix.
The posters for V for Vendetta read, An uncompromising vision of the future from the creators of The Matrix trilogy'.
The posters for V for Vendetta read "An uncompromising vision of the future from the creators of The Matrix trilogy".
At NAB, Riedel Communications unveils its new Artist VoIP-108 G2 client card, which converts eight matrix ports into a compressed IP-stream and vice versa.
Increasing Cellular Communication for Skin Matrix Repair.
Matrix Concepts and 1.7 Cleaning Solutions has completed the move into their new corporate headquarters in Valencia, California.
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In science:

Matrixes a and b are bosonic square matrix while α and β generally are not square matrix.
Gauge Theory of Gravity
All matrix elements with α = α′ and β 6= β ′ which couple the block matrix Mα,β (d, d′ ) to the other components of the matrix M(i) vanish by the superselection rules and δαβ δα′ β ′ = 0.
Superpenetration of a high energy Q barQ bound state through random color fields
Here we diagonalized the matrix Ω and integrated out the corresponding eigenvectors with the use the IZHC formula Eq.(28), with ǫ > 0 (∝ unity matrix) being an infinitesimal regularisation matrix.
Random Matrices close to Hermitian or unitary: overview of methods and results
Sometimes these tau-functions can be written in terms of the matrix integrals (about appearance of the Virasoro constraints in matrix models and the relation between the matrix models and integrable systems see, for example, ).
String Theory or Field Theory?
Equivalently, one may say that there must be some orthogonal matrix Q such that the associated matrix T defined by the relation (15) is a sparse matrix with at most k nonvanishing elements on any line.
Random Series and Discrete Path Integral methods: The Levy-Ciesielski implementation
P S 2 · S )/6 TABLE III: Matrix formulas for the numbers of all 3-node connected directed subgraphs. M is the adjacency matrix, S is its symmetric component, and A its asymmetric component. A′ is the transposed matrix, eA is the logical inverse of matrix A, trA is the matrix trace.
Subgraphs in random networks
A and B , and by A · B the dot multiplication. the logical inverse of matrix A, where the 0 elements of A are the 1 of eA and vice-versa. A′ is the transpose matrix of A. A summation denotes summation of all the matrix indices.
Subgraphs in random networks
The quantum operator ˆX ∈ L(V ) cotangent space T⋆ can be represented in the given basis by a matrix X ∈ MATRIX(N , N , F) with matrix elements Xij ∈ F, where MATRIX(N , N , F) is set of all N × N matrices with elements from the field F.
Quantum fluctuations and random matrix theory
It has the analogical random matrix variable X : Ω ∋ ω → X (ω ) ∈ MATRIX(N , N , F), where X = X (ω ) is deterministic matrix [1, 2, 3].
Quantum fluctuations and random matrix theory
The Hamiltonian matrix H is hermitean N × N F-matrix, and the matrix Haar’s measure dH is invariant under transformations from the unitary group U(N , F).
Quantum fluctuations and random matrix theory
The matrix regularization replaces the dependence on the spatial coordinates by matrix degrees of freedom, and the regularized theory becomes a matrix quantum mechanics.
Perturbative dynamics of matrix string for the membrane
Hence, the quantum wrapped membrane will be defined by matrix string theory with the matrix variables obeying the twisted boundary condition (2.17), instead of the periodic one used in the original matrix string theory .
Perturbative dynamics of matrix string for the membrane
It is nevertheless an important fact that possibility to perform the ensemble average explicitly exists whenever matrix entries of H are Gaussian-distributed, not requiring any matrix invariance or even independence of the matrix entries.
Complexity of Random Energy Landscapes, Glass Transition and Absolute Value of Spectral Determinant of Random Matrices
The eigenvalue equation of a complex Hermitian matrix H is given by H U = U Λ with Λ as the matrix of eigenvalues λn and U as the eigenvector matrix, unitary in nature.
Random Matrices with Correlated Elements: A Model for Disorder with Interactions
Here M , C , K can be finite symmetric matrices, with the mass matrix M positive semidefinite, the stiffness matrix K positive definite and the damping matrix C accretive1 (our result seems to be new even in the matrix case).
Bounds for contractive semigroups and second order systems
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