For many years a state tax on cities and towns was paid by the several municipalities to the state from the proceeds of the general property tax.

For the policy officer will know that action can almost never be secret and that in general the effectiveness of policy will be conditioned by the readiness of the country to sustain it.

For the near term, however, it must be realized that the industrial and commercial market is somewhat more sensitive to general business conditions than is the military market, and for this reason I would expect that any gain in 1961 may be somewhat smaller than those of recent years ; ;

For any pencil in a plane containing a Af-fold secant of **zg has an image regulus which meets the plane of the pencil in Af lines, namely the images of the lines of the pencil which pass through the intersection of **zg and the multiple secant, plus an additional component to account for the intersections of the images of the general lines of the pencil.

For many of these unwed mothers, the data on their family life and early childhood experiences revealed several indications and sources of their basic mistrust of their parents in particular and of the world in general.

-- For a second month in a row, Multnomah County may be short of general assistance money in its budget to handle an unusually high summer month's need, the state public welfare commission was told Friday.

For general morale reasons and to encourage the efforts of his supply officers, when food was short for combat troops he cut the rations of his headquarters staff accordingly.

For this latest addition to the Great Letters Series, under the general editorship of Louis Kronenberger, Miss Hardwick has made a selection which admirably displays the variety of James's genius, not to mention the felicities of his style.

* For the general reader.

For general computer use access technology such as screen readers, screen magnifiers and refreshable Braille displays has been widely taken up along with standalone reading aids that integrate a scanner, optical character recognition ( OCR ) software, and speech software in a single machine.

For biologists, this includes human beings, although for the general public the term " animal " means only non-human animals.

For example, in some groups, the group operation is commutative, and this can be asserted with the introduction of an additional axiom, but without this axiom we can do quite well developing ( the more general ) group theory, and we can even take its negation as an axiom for the study of non-commutative groups.

For other uses, see Alexander and Alexander ( Aetolian general )

For Hume, philosophy can be split into two general parts: natural philosophy and the philosophy of human nature ( or, as he calls it, " moral philosophy ").

For the frequent case of propositional logic, the problem is decidable but Co-NP-complete, and hence only exponential-time algorithms are believed to exist for general proof tasks.

For example, if James's will states that he is leaving $ 500, 000 to his son Sam then the money would be a general devise.

For years, it was traded privately until a ROM was made available to the general public.

For example, abstracting a leather soccer ball to the more general idea of a ball retains only the information on general ball attributes and behavior, eliminating the other characteristics of that particular ball.

For this reason, players should choose badminton shoes rather than general trainers or running shoes, because proper badminton shoes will have a very thin sole, lower a person's centre of gravity, and therefore result in fewer injuries.

For many years, the U. S. has borrowed and bought while in general, the rest of the world has lent and sold.

For several decades from the 1970s to early 2000s, the focus in designing high performance general purpose CPUs was largely on achieving high ILP through technologies such as pipelining, caches, superscalar execution, out-of-order execution, etc.

For example, the Napoleonic code expressly forbade French judges from pronouncing general principles of law.

For example, the copyright to a Mickey Mouse cartoon restricts others from making copies of the cartoon or creating derivative works based on Disney's particular anthropomorphic mouse, but does not prohibit the creation of other works about anthropomorphic mice in general, so long as they are different enough to not be judged copies of Disney's.

For many decades, consciousness as a research topic was avoided by the majority of mainstream scientists, because of a general feeling that a phenomenon defined in subjective terms could not properly be studied using objective experimental methods.

For square matrices with entries in a non-commutative ring, for instance the quaternions, there is no unique definition for the determinant, and no definition that has all the usual properties of determinants over commutative rings.

For example, the proof that the column rank of a matrix over a field equals its row rank yields for matrices over division rings only that the left column rank equals its right row rank: it does not make sense to speak about the rank of a matrix over a division ring.

For example Sp ( 8 ) has a representation in terms of 4x4 quaternion unitary matrices which has a 16 dimensional real representation and so might be considered as a candidate for a gauge group.

For example, the orthogonal group O < sub > n </ sub >( R ) consists of matrices A with AA < sup > T </ sup > = 1, so the Lie algebra consists of the matrices m with ( 1 + εm )( 1 + εm )< sup > T </ sup > = 1, which is equivalent to m + m < sup > T </ sup > = 0 because ε < sup > 2 </ sup > = 0.

For example, it is not rare to find studies with character matrices based on whole mitochondrial genomes (~ 16, 000 nucleotides, in many animals ).

For example, methods based on covariance matrices are typically employed on the premise that numbers, such as raw scores derived from assessments, are measurements.

For this reason, positive definite matrices play an important role in optimization problems.

For arbitrary square matrices M, N we write M ≥ N if M − N ≥ 0 ; i. e., M − N is positive semi-definite.

For those media in which the amplitudes are unchanged but a differential phase delay occurs, the Jones matrix is unitary, while those affecting amplitude without phase have Hermitian Jones matrices.

For instance, the general linear group GL ( n, R ) of all invertible n-by-n matrices with real entries can be viewed as a topological group with the topology defined by viewing GL ( n, R ) as a subset of Euclidean space R < sup > n × n </ sup >.

For this reason, generalizations of vector operations to matrices ( e. g. in matrix calculus and statistics ) often involve a trace of matrix products.

For this reason, fuzzy logic usually uses IF-THEN rules, or constructs that are equivalent, such as fuzzy associative matrices.

For a linear continuous-time system, like the example above, described by matrices,,, and, the output controllability matrix

For example, quantitative preparative native continuous polyacrylamide gel electrophoresis ( QPNC-PAGE ) is a method for separating native metalloproteins in complex biological matrices.

For example, it is often desirable to compute an orthonormal basis for a space, or an orthogonal change of bases ; both take the form of orthogonal matrices.

For example, the general linear group over R ( the set of real numbers ) is the group of n × n invertible matrices of real numbers, and is denoted by GL < sub > n </ sub >( R ) or GL ( n, R ).

For quaternion scalars and matrices:

For two matrices

For diagonalizable matrices, an even better method is to use the eigenvalue decomposition of A.

For two matrices of the same dimensions, there is the Hadamard product, also known as the entrywise product and the Schur product.

For two matrices A and B of the same dimensions, the Hadamard product A ○ B is a matrix of the same dimensions, which has elements

For two matrices A and B of any different dimensions m × n and p × q respectively ( no contraints on the dimensions of each matrix ), the Kronecker product denoted A ⊗ B is a matrix with dimensions mp × nq, which has elements

* For any positive integer n, the set of all n by n unitary matrices with matrix multiplication forms a group, called the unitary group U ( n ).