A matrix can have a considerable effect on the way a chemical analysis is conducted and the quality of its results.

The primary metal is called the base, the matrix, or the solvent.

Steel is an example of an interstitial alloy, because the very small carbon atoms fit into interstices of the iron matrix.

In the < tt > SubBytes </ tt > step, each byte in the state matrix is replaced with a < tt > SubByte </ tt > using an 8-bit substitution box, the Rijndael S-box.

During this operation, each column is multiplied by the known matrix that for the 128 bit key is

If there are proteins left in the shell matrix, it is also possible that they can trigger an allergic ( asthmatic ) attack.

The outer surface of an agate, freed from its matrix, is often pitted and rough, apparently in consequence of the removal of the original coating.

The fundamental unit of the aorta is the elastic lamella, which consists of smooth muscle and elastic matrix.

Standard addition can be applied to most analytical techniques and is used instead of a calibration curve to solve the matrix effect problem.

* Pyrolysis – the majority of the matrix constituents is removed

* Use of a chemical modifier in order to stabilize the analyte to a pyrolysis temperature that is sufficient to remove the majority of the matrix components ;

Another source of background absorption, particularly in ET AAS, is scattering of the primary radiation at particles that are generated in the atomization stage, when the matrix could not be removed sufficiently in the pyrolysis stage.

The osteiod seam is a narrow region of newly formed organic matrix, not yet mineralized, located on the surface of a bone.

The majority of bone is made of the bone matrix.

Bone is formed by the hardening of this matrix entrapping the cells.

The matrix is initially laid down as unmineralised osteoid ( manufactured by osteoblasts ).

The organic part of matrix is mainly composed of Type I collagen.

One of the main things that distinguishes the matrix of a bone from that of another cell is that the matrix in bone is hard.

Woven bone is weaker, with a smaller number of randomly oriented collagen fibers, but forms quickly ; it is for this appearance of the fibrous matrix that the bone is termed woven.

A matrix that is not invertible has the condition number equal to infinity.

Thus for instance the determinant of a matrix with integer coefficients will be an integer, and the matrix has an inverse with integer coefficients if and only if this determinant is 1 or − 1 ( these being the only invertible elements of the integers ).

If G = GL < sub >*</ sub >( K ), then the set of natural numbers is a proper subset of G < sub > 0 </ sub >, since for each natural number n, there is a corresponding identity matrix of dimension n. G ( m, n ) is empty unless m = n, in which case it is the set of all nxn invertible matrices.

It can also be used to find the rank of a matrix, to calculate the determinant of a matrix, and to calculate the inverse of an invertible square matrix.

The three elementary row operations used in the Gaussian elimination ( multiplying rows, switching rows, and adding multiples of rows to other rows ) amount to multiplying the original matrix with invertible matrices from the left.

The first part of the algorithm computes an LU decomposition, while the second part writes the original matrix as the product of a uniquely determined invertible matrix and a uniquely determined reduced row-echelon matrix.

As explained above, Gaussian elimination writes a given m × n matrix A uniquely as a product of an invertible m × m matrix S and a row-echelon matrix T. Here, S is the product of the matrices corresponding to the row operations performed.

* The group GL < sub > n </ sub >( R ) of invertible matrices ( under matrix multiplication ) is a Lie group of dimension n < sup > 2 </ sup >, called the general linear group.

For determinantal rank, the statement is that if the row rank ( column rank ) of a matrix is p, then one can choose a p × p submatrix that is invertible: a subset of the rows and a subset of the columns simultaneously define an invertible submatrix.

* If A is a square matrix ( i. e., m = n ), then A is invertible if and only if A has rank n ( that is, A has full rank ).

* The rank of A is equal to r if and only if there exists an invertible m-by-m matrix X and an invertible n-by-n matrix Y such that

Mathematically, if the coordinate system undergoes a transformation described by an invertible matrix M, so that a coordinate vector x is transformed to x ′

< li > Every positive definite matrix is invertible and its inverse is also positive definite.

A square matrix with entries in a field is invertible ( in the set of all square matrices of the same size, under matrix multiplication ) if and only if its determinant is different from zero.

Their functions include, to varying degrees: formation of bone ; matrix maintenance ; and calcium homeostasis.

I want to see institutions like Throop turn out perhaps ninety-nine of every hundred students as men who are to do given pieces of industrial work better than any one else can do them ; I want to see those men do the kind of work that is now being done on the Panama Canal and on the great irrigation projects in the interior of this country — and the one-hundredth man I want to see with the kind of cultural scientific training that will make him and his fellows the matrix out of which you can occasionally develop a man like your great astronomer, George Ellery Hale.

Note that this is before the effects of round-off error are taken into account ; conditioning is a property of the matrix, not the algorithm or floating point accuracy of the computer used to solve the corresponding system.

where A is a 2 × 2 orthogonal matrix and b = ( b < sub > 1 </ sub >, b < sub > 2 </ sub >) is an arbitrary ordered pair of numbers ; that is,

This core memory board, Part Number 50823 D8 7504-14166, and with layout artwork copyrighted 1971 by DGC, was organized in planar fashion as four groups of four banks, each bank carrying two sets of core in a 64 by 64 matrix ; thus there were 64 x 64 = 4096 bits per set, x 2 sets giving 8, 192 bits, x 4 banks giving 32, 768 bits, x 4 goups giving a total of 131, 072 bits, and this divided by the machine word size of 16 bits gave 8, 192 Words of memory.

The transform is sometimes denoted by the symbol, as in or or < ref group =" note "> As a linear transformation on a finite-dimensional vector space, the DFT expression can also be written in terms of a DFT matrix ; when scaled appropriately it becomes a unitary matrix and the X < sub > k </ sub > can thus be viewed as coefficients of x in an orthonormal basis .</ ref >

( Note that there are N independent eigenvectors ; a unitary matrix is never defective.

Logical matrix | Logical matrices of the Bell number | 52 equivalence relations on a 5-element set ( Colored fields, including those in light gray, stand for ones ; white fields for zeros.

To distinguish the degenerate cases from the non-degenerate case, let ∆ be the determinant of the 3 × 3 matrix B / 2, D / 2 ; B / 2, C, E / 2 ; D / 2, E / 2, F: that is, ∆

; Incidence matrix: The graph is represented by a matrix of size | V | ( number of vertices ) by | E | ( number of edges ) where the entry edge contains the edge's endpoint data ( simplest case: 1-incident, 0-not incident ).

; Adjacency matrix: This is an n by n matrix A, where n is the number of vertices in the graph.

; Laplacian matrix or " Kirchhoff matrix " or " Admittance matrix ": This is defined as D − A, where D is the diagonal degree matrix.

; Distance matrix: A symmetric n by n matrix D, where n is the number of vertices in the graph.

The high ionic radius of the Pb < sup > 2 +</ sup > ion renders it highly immobile in the matrix and hinders the movement of other ions ; lead glasses therefore have high electrical resistance, about two orders of magnitude higher than soda-lime glass ( 10 < sup > 8. 5 </ sup > vs 10 < sup > 6. 5 </ sup > Ohm · cm, DC at 250 ° C ).