From such uncertainties, that characterize ongoing work, stems the unavailability of a definition of algorithm that suits both concrete ( in some sense ) and abstract usage of the term.

From the above, it is possible to reformulate the definition to either of the following:

From 1975 to 1979, a Canadian progressive power trio, Rush, released three albums containing sidelong epics, regarded by some as concept albums ( though not actually concept albums by strict definition of the term ; that is, none of the other songs on the album have anything to do with each other or the 20-minute sidelong epic, so there is no pervasive concept or story ).

The result, div F, is a function of p. From this definition it also becomes explicitly visible that div F can be seen as the source density of the flux of F.

From his first composition to his last, he rejected the idea of musical development, in the strict definition of this term: the intertwining of different themes in a development section of a sonata form.

From earliest times, some kind of government has arguably been a vital part of every human society — though this refers only to a particularly loose definition of government.

From these three assumptions, neoclassical economists have built a structure to understand the allocation of scarce resources among alternative ends — in fact understanding such allocation is often considered the definition of economics to neoclassical theorists.

From the definition of the delta-function, u may also be written as

From the definition, the direction of the electric field is the same as the direction of the force it would exert on a positively-charged particle, and opposite the direction of the force on a negatively-charged particle.

From the definition of ( angular ) wavenumber ;

From the 19th century, a large portion of the Muslim peoples ( termed ' Muhacir ' under a general definition ) of the Balkans, Caucasus, Crimea and Crete took refuge in present-day Turkey and shaped that country's fundamental features.

From Aristotle onward the definition, in philosophical contexts, of the word " essence " is very close to the definition of form ( Gr. morphe ).

From this definition, it is straightforward to find an equivalent charge in SI coulombs.

From the circuit diagram to the right, according to Kirchoff's Laws and the definition of capacitance:

From the circuit in Figure 1 above, according to Kirchoff's Laws and the definition of capacitance:

From Rüssspitz to Wildspitz, from Chiem to Gottschalkenberg, one can discover many scenic highlights ; for example, the Zugerberg mountain and the Walchwilerberg Oberallmig-a ridge of fascinating depth of definition, a moor with national cachet.

From the definition of the magnetic vector potential A and the fundamental theorem of the curl the magnetic flux may also be defined as:

From this, Post was able to derive the following definition of inconsistency without the use of the notion of contradiction:

In convex geometry, a face of a polytope P is the intersection of any supporting hyperplane of P and P. From this definition it follows that the set of faces of a polytope includes the polytope itself and the empty set.

From this follows the definition of effective mass:

From this definition, the latent heat for a given mass of a substance is calculated by

From the Bronze Age into the Renaissance the average masses of wheat and barley grains were part of the legal definition of units of mass.

From this definition, several other properties can be deduced.

From 1981 onwards the IBM PC's introduction of " Code page 437 " with 254 printable glyphs ( including 40 shapes specifically for drawing forms ), and development of Xerox Star-influenced environments such as the Macintosh, GEM and Windows made bit-mapped approaches more desirable, driving cost reductions for laser printing and higher resolution for impact dot matrix printing.

From a mathematical perspective, the diagrams are a concise way to represent multilinear functions and functions between representations of matrix groups.

From this one can deduce that a square matrix A is invertible if and only if A < sup > T </ sup > is invertible, and in this case we have ( A < sup >− 1 </ sup >)< sup > T </ sup >

From 1923 to 1938, Weyl developed the theory of compact groups, in terms of matrix representations.

From this formula follows one of the most important results in matrix algebra: A matrix A over a commutative ring R is invertible if and only if det ( A ) is invertible in R.

From the confusion matrix you can derive four basic measures

From this point of view, we can define the Pseudo-determinant for a singular matrix to be the product of all the nonzero eigenvalues ( the density of Multivariate normal distribution will need this quantity ).

From this he developed a set of 40 inventive principles and later a matrix of contradictions.

From 1931 he also worked for the Pravda newspaper, distributing its matrix from Moscow to other cities by the air.

From this, the generator matrix G can be obtained as ( noting that in the special case of this being a binary code ), or specifically:

From the definition it follows that any totally unimodular matrix has only 0, + 1 or − 1 entries.

From this point of view, the approximated matrix is interpreted as a de-noisified matrix ( a better matrix than the original ).

From linear algebra one knows that a certain matrix can be represented in another basis through the transformation

From this point of view, quaternionic representation of a group G is a group homomorphism φ: G → GL ( V, H ), the group of invertible quaternion-linear transformations of V. In particular, a quaternionic matrix representation of g assigns a square matrix of quaternions ρ ( g ) to each element g of G such that ρ ( e ) is the identity matrix and

From these properties we can show that a rotation is a linear transformation of the vectors, and thus can be written in matrix form, Qp.

From 1888 to 1890, Killing essentially classified the complex finite dimensional simple Lie algebras, inventing the notions of a Cartan subalgebra and the Cartan matrix.

From an initial guess and an approximate Hessian matrix the following steps are repeated until converges to the solution.

From the estimated rate matrix, a series of replacement probability matrices were derived, known under names such as PAM250.