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.

Thus a 2 × 2 matrix with determinant − 2, when applied to a region of the plane with finite area, will transform that region into one with twice the area, while reversing its orientation.

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 ).

By placing the molecules in wells in the gel and applying an electric field, the molecules will move through the matrix at different rates, determined largely by their mass when the charge to mass ratio ( Z ) of all species is uniform, toward the ( negatively charged ) cathode if positively charged or toward the ( positively charged ) anode if negatively charged.

The boson matrix will have a boson or its new partner in each row and column.

Upon completion of this procedure the augmented matrix will be in row-echelon form and may be solved by back-substitution.

The matrix can be reused to create hundreds, or thousands, of identical sorts so that the same character appearing anywhere within the book will appear very uniform, giving rise, over time, to the development of distinct styles of typefaces or fonts.

Therefore, the spin angular velocity vector () about the spin axis will have to evolve in time so that the matrix product remains constant.

Its diagonal entries will be eigenvalues corresponding to certain linear combinations of certain subsets of sequences which will be eigenvectors of the W matrix.

Assuming that the matrix W is irreducible, then after very many generations only the eigenvector with the largest eigenvalue will prevail, and it is this quasispecies that will eventually dominate.

where R < sub > i </ sub >< sup > j </ sup > is a matrix and in the second expression the summation sign was suppressed ( a notational convenience introduced by Einstein that will be used throughout this article ).

This matrix will also be found to anticommute with the other four Dirac matrices.

Under certain conditions on, the reduced matrix will be positive definite.

Autolysins are naturally produced by peptidoglycan containing bacteria, but excessive amounts will degrade the peptidoglycan matrix and cause the cell to burst due to osmotic pressure.

DASCOM will continue to resell TallyGenicom-branded line matrix and laser products purchased from Printronix, and Printronix will resell serial matrix products purchased from DASCOM.

( In this case, ' large ' means, approximately, more than 100, 000 elements in each matrix, or enough addressable memory such that the matrices will not fit in L1 and L2 caches.

Since it was quite easy to stack interconnections ( wires ) inside the embedding matrix, the approach allowed designers to forget completely about the routing of wires ( usually a time-consuming operation of PCB design ): Anywhere the designer needs a connection, the machine will draw a wire in straight line from one location / pin to another.

Where the wave equation is represented as a complex vector, the probability will be extracted from the absolute value of an inner-product of the coefficient matrix and its complex conjugate.

So that the total probability will be preserved, K is what is called a stochastic matrix.

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

AES operates on a 4 × 4 column-major order matrix of bytes, termed the state, although some versions of Rijndael have a larger block size and have additional columns in the state.

* Osteocytes originate from osteoblasts that have migrated into and become trapped and surrounded by bone matrix that they themselves produce.

For example, when an ordinary RGB digital image is compressed via the JPEG standard, the RGB colorspace is first converted ( by a rotation matrix ) to a YCbCr colorspace, because the three components in that space have less correlation redundancy and because the chrominance components can then be subsampled by a factor of 2 or 4 to further compress the image.

To be orthogonal, the matrix A must have orthogonal rows with same Euclidean length of one, that is,

To avoid triggering unwanted notes, most keyboard matrix circuits have diodes soldered with the switch under each key of the musical keyboard.

Since there are only four distinct eigenvalues for this matrix, they have some multiplicity.

The sample data matrix must have full rank or OLS cannot be estimated.

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 ).

If he used the punch and matrix approach, all his letters should have been nearly identical, with some variations due to miscasting and inking.

While some identical types are clearly used on other pages, other variations, subjected to detailed image analysis, suggested that they could not have been produced from the same matrix.

They hypothesized that the method may have involved impressing simple shapes to create alphabets in " cuneiform " style in a matrix made of some soft material, perhaps sand.

The 19th century printer and typefounder Fournier Le Jeune suggested that Gutenberg might not have been using type cast with a reusable matrix, but possibly wooden types that were carved individually.

They have one-piece plastic keytop / switch plungers which press down on a membrane to actuate a contact in an electrical switch matrix.

If G is any subgroup of GL < sub > n </ sub >( R ), then the exponential map takes the Lie algebra of G into G, so we have an exponential map for all matrix groups.

These plastic casings are usually a composite material made up of a thermoplastic matrix such as acrylonitrile-butadiene-styrene ( ABS ) in which calcium carbonate chalk, talc, glass fibers or carbon fibers have been added for added strength, bulk, or electrostatic dispersion.

Albert Eulenburg ( 1914 ) noted a commonality across the paraphilias, using the terminology of his time, " All the forms of sexual perversion ... have one thing in common: their roots reach down into the matrix of natural and normal sex life ; there they are somehow closely connected with the feelings and expressions of our physiological erotism.

However, simulations have shown that it is more important to increase the number of taxa in the matrix than to increase the number of characters, because the more taxa there are, the more accurate and more robust is the resulting phylogenetic tree.

The rank of an m × n matrix cannot be greater than m nor n. A matrix that has a rank as large as possible is said to have full rank ; otherwise, the matrix is rank deficient.

* Arenites are texturally " clean " sandstones that are free of or have very little matrix.

If the condition number is close to one, the matrix is well conditioned which means its inverse can be computed with good accuracy.

Practically, such a matrix is almost singular, and the computation of its inverse, or solution of a linear system of equations is prone to large numerical errors.

The determinant provides important information when the matrix is that of the coefficients of a system of linear equations, or when it corresponds to a linear transformation of a vector space: in the first case the system has a unique solution if and only if the determinant is nonzero, while in the second case that same condition means that the transformation has an inverse operation.

The inverse transform is then given by the inverse of the above matrix:

This can be seen from the inverse properties above: operating twice gives the original data in reverse order, so operating four times gives back the original data and is thus the identity matrix.

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 components, v < sup > i </ sup >, of a regular ( or column ) vector, v, transform with the inverse of the matrix R,

In the matrix representation, the inverse is:

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

( The identity matrix itself is invertible, being its own inverse.

The identity matrix also has the property that, when it is the product of two square matrices, the matrices can be said to be the inverse of one another.

Since is a rotation matrix its inverse is its transpose.

If the errors are correlated, the resulting estimator is BLUE if the weight matrix is equal to the inverse of the variance-covariance matrix of the observations.

Then, the inverse of this matrix is S, the lower triangular matrix of Stirling numbers of second kind.

Equivalently, a matrix Q is orthogonal if its transpose is equal to its inverse:

An orthogonal matrix Q is necessarily invertible ( with inverse ), unitary (), and normal ().

A reflection is its own inverse, which implies that a reflection matrix is symmetric ( equal to its transpose ) as well as orthogonal.

The inverse of every orthogonal matrix is again orthogonal, as is the matrix product of two orthogonal matrices.