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for all vectors w. Conversely, each covector α determines a unique vector v by this equation.
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for and all
He knew who was riding after him -- the men he had known all his life, the men who had worked for him, sworn their loyalty to him.
It poured out of him like an electric current, a feeling that the muscles and nerves of his fine-drawn body were coiling for action, and that that action would be all that he anticipated.
It is possible, although highly doubtful, that he killed none at all but merely let his reputation work for him by privately claiming every unsolved murder in the state.
`` Soon as we send them on their way and make camp, let's you and me go for a walk down by the Snake -- all by ourselves ''.
Seeing them waiting there at the foot of Emigrant Rock was so overwhelming that, for a good minute after they rounded the bend and started down the grade leading toward them, Matilda could not speak at all.
There were no less than six or seven saloons in Ganado, not counting the lower class dives, all vying for the trade of celebrating miners and teamsters.
this is not so, for education offers all kinds of dividends, including how to pull the wool over a husband's eyes while you are having an affair with his wife.
Packing a small suitcase, informing her husband whom she found in Harry's Bar that she was taking a train to Germany to get away for a while, patting his arm, refusing a drink, getting on the train -- all this had only taken her two hours.
At the same time, all suggestions that some sort of societal responsibility existed for the welfare of the people within the territorial state was strongly resisted.
For better or for worse, we all now live in welfare states, the organizing principle of which is collective responsibility for individual well-being.
These songs ( practically all Persian music, for that matter ) are limited to a range of two octaves.
`` As an independent American I considered all who were not for us, and you amongst the rest, as against us, yet be assured that John Jay never ceased to be the friend of Peter Van Schaack ''.
for and vectors
We can do this through the characteristic values and vectors of T in certain special cases, i.e., when the minimal polynomial for T factors over the scalar field F into a product of distinct monic polynomials of degree 1.
Second, even if the characteristic polynomial factors completely over F into a product of polynomials of degree 1, there may not be enough characteristic vectors for T to span the space V.
For vector spaces over non-algebraically closed fields, we still need to find some substitute for characteristic values and vectors.
( Technically, the quantum states are rays of vectors in the Hilbert space, as corresponds to the same state for any nonzero complex number c .)
The great utility in creating CPUs that deal with vectors of data lies in optimizing tasks that tend to require the same operation ( for example, a sum or a dot product ) to be performed on a large set of data.
where are the coordinate vectors in some frame of reference chosen for the problem ( See figure 1 ).
A displacement field is a vector field of all displacement vectors for all particles in the body, which relates the deformed configuration with the undeformed configuration.
Additionally, small rodents, including squirrels, mice, and rats, are important in the sylvatic transmission cycle because of their importance as bloodmeal sources for the insect vectors.
( Although mutual orthogonality is the only condition, these vectors are usually constructed for ease of decoding, for example columns or rows from Walsh matrices.
Polar unit vectors at two times t and t + dt for a particle with trajectory r ( t ); on the left the unit vectors u < sub > ρ </ sub > and u < sub > θ </ sub > at the two times are moved so their tails all meet, and are shown to trace an arc of a unit radius circle.
This coordinate system sometimes is referred to as intrinsic or path coordinates or nt-coordinates, for normal-tangential, referring to these unit vectors.
As for the other examples above, because unit vectors cannot change magnitude, their rate of change is always perpendicular to their direction ( see the left-hand insert in the image above ):
:: < nowiki > the use of row vectors for point coordinates and that the matrix is written on the right .< nowiki ></ nowiki >
Many high-level programming languages, and some higher-level assembly languages, such as MASM, on the other hand, have special syntax or other built-in support for certain data structures, such as vectors ( one-dimensional arrays ) in the C language or multi-dimensional arrays in Pascal.
In other words, for any N > 0, an N-dimensional complex vector has a DFT and an IDFT which are in turn N-dimensional complex vectors.
If y is a point where the vector field v ( y ) ≠ 0, then there is a change of coordinates for a region around y where the vector field becomes a series of parallel vectors of the same magnitude.
By 1951, 87 subroutines in the following categories were available for general use: floating point arithmetic ; arithmetic operations on complex numbers ; checking ; division ; exponentiation ; routines relating to functions ; differential equations ; special functions ; power series ; logarithms ; miscellaneous ; print and layout ; quadrature ; read ( input ); nth root ; trigonometric functions ; counting operations ( simulating repeat until loops, while loops and for loops ); vectors ; and matrices.
The greatest common divisor is often written as GCD ( a, b ) or, more simply, as ( a, b ), although the latter notation is also used for other mathematical concepts, such as two-dimensional vectors.
Given also a measure on set, then, sometimes also denoted or, has as its vectors equivalence classes of measurable functions whose absolute value's-th power has finite integral, that is, functions for which one has
0.283 seconds.