If T is a linear operator on an arbitrary vector space and if there is a monic polynomial P such that Af, then parts ( A ) and ( B ) of Theorem 12 are valid for T with the proof which we gave.

Under equilibrium conditions of cutting the chip exerts a thrust Af against the knife which tends to push it into the substrate or lift it away from the substrate depending on the vector direction of Af.

This means that the game graphics are composed entirely of lines which are drawn on a vector monitor.

The hardware consists primarily of a standard MOS 6502 CPU, which executes the game program, and the Digital Vector Generator ( DVG ), vector processing circuitry developed by Atari themselves.

Many theorems which are provable using choice are of an elegant general character: every ideal in a ring is contained in a maximal ideal, every vector space has a basis, and every product of compact spaces is compact.

Atomic orbitals are typically categorized by n, l, and m quantum numbers, which correspond to the electron's energy, angular momentum, and an angular momentum vector component, respectively.

The fertilized macrogamete now becomes an ookinete which penetrates the body of the vector.

At the instant of any observation of an object, the apparent position of the object is displaced from its true position by an amount which depends solely upon the transverse component of the velocity of the observer, with respect to the vector of the incoming beam of light ( i. e., the line actually taken by the light on its path to the observer ).

which may promote viral survival and vector longevity during milder winters.

This is in contrast to the original C. imicola vector which is limited to North Africa and the Mediterranean.

A new gene is inserted into an adenovirus vector, which is used to introduce the modified DNA into a human cell.

A special case is the inner product of a vector with itself, which is square of its norm ( magnitude ):

must be the unit operator, which sends each vector to itself.

This was a slow process which happened naturally through normal spreading of trade, with the silk and spice trade via the Silk Road being the prime vector.

A plotter is a vector graphics printing device which operates by moving a pen over the surface of paper.

Plotters have been used in applications such as computer-aided design, though they are rarely used now and are being replaced with wide-format conventional printers, which nowadays have sufficient resolution to render high-quality vector graphics using a rasterized print engine.

Thus, body forces are specified by vector fields which are assumed to be continuous over the entire volume of the body, i. e. acting on every point in it.

Body forces are represented by a body force density ( per unit of mass ), which is a frame-indifferent vector field.

which is a mapping of the initial configuration onto the current configuration, giving a geometrical correspondence between them, i. e. giving the position vector that a particle, with a position vector in the undeformed or reference configuration, will occupy in the current or deformed configuration at time.

The material derivative of any property of a continuum, which may be a scalar, vector, or tensor, is the time rate of change of that property for a specific group of particles of the moving continuum body.

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.

In the language of linear transformations, D < sub > a </ sub >( g ) is the function which scales a vector by a factor of g ′( a ) and D < sub > g ( a )</ sub >( f ) is the function which scales a vector by a factor of f ′( g ( a )).

In physics and mathematics, a pseudovector ( or axial vector ) is a quantity that transforms like a vector under a proper rotation, but gains an additional sign flip under an improper rotation such as a reflection.

Large gains are possible since any particular test vector usually only needs to set and / or examine a small fraction of the scan chain bits.

The minus (-) sign comes from the fact that the force is considered towards the surface element, while the normal vector points outward.

If the world is reflected in a mirror which switches the left and right side of the car, the reflection of this angular velocity vector points to the right, but the actual angular velocity vector of the wheel still points to the left, corresponding to the minus sign.

If only b is a unit vector, then the dot product a · b gives || a || cos θ, i. e., the magnitude of the projection of a in the direction of b, with a minus sign if the direction is opposite.

If the world is reflected in a mirror which switches the left and right side of the car, the " reflection " of this angular momentum " vector " ( viewed as an ordinary vector ) points to the right, but the actual angular momentum vector of the wheel still points to the left, corresponding to the extra minus sign in the reflection of a pseudovector.

# First, three of these terms are associated with sign ambiguities: the line integral could go around the loop in either direction ( clockwise or counterclockwise ); the vector area dS could point in either of the two directions normal to the surface ; and I < sub > enc </ sub > is the net current passing through the surface S, meaning the current passing through in one direction, minus the current in the other direction — but either direction could be chosen as positive.

For convenience it is often defined as minus the potential energy per unit mass, so that the gravity vector is obtained as the gradient of this potential, without the minus.

The headwind velocity in still air is inverse of the object's velocity, therefore the apparent wind can also be defined as a vector subtraction: the Velocity of the wind minus the Velocity of the object.

particularly since both the scalar Laplacian, and the matrix, A are linear operators on their respective function / vector spaces ( the minus sign in the second equation is, for all intents and purposes, immaterial ; the plus sign in the first equation however is significant ).

All vector transformations, scale, rotation and positioning ( minus skewing ) have keyboard shortcuts with consistent modifiers, e. g., Alt transforms by 1 screen pixel at the current zoom, Shift multiplies the transformation by 10, etc.

which, written out in vector components is given by This result is similar to what we wish to evince in vector terms ’ except ’ for the minus sign.

The instrument had three ranges covering plus or minus 20, 60, and 200 nT full scale for each vector component.

The scalar projection is equal to the length of the vector projection, with a minus sign if the direction of the projection is opposite to the direction of.

However, George Sudarshan and Robert Marshak were the first proponents of the successful V-A ( vector minus axial vector, or left-handed ) theory for weak interactions in 1957.

In mathematics, a complex structure on a real vector space V is an automorphism of V that squares to the minus identity, − I.

The interaction term has a V-A ( vector minus axial ) form.

It is a vector, parallel to the bond axis, pointing from minus to plus, as is conventional for electric dipole moment vectors.

( Some chemists draw the vector pointing from plus to minus, but only in situations where the direction is not important.