For example, a Givens rotation affects only two rows of a matrix it multiplies, changing a full multiplication of order n < sup > 3 </ sup > to a much more efficient order n. When uses of these reflections and rotations introduce zeros in a matrix, the space vacated is enough to store sufficient data to reproduce the transform, and to do so robustly.

When he meets his new boss, Jacqueline Broyer ( Robin Givens ), Marcus discovers that she is essentially a female version of himself, and realizes he is receiving the same treatment that he delivers to others.

When the platform is level, **ye is a rotation about the Z axis of the platform Af.

When the rate of rotation is made constant in the analysis of nonuniform circular motion, that analysis agrees with this one.

When pointing the thumb away from the origin along an axis, the curvature of the fingers indicates a positive rotation along that axis.

When one arm is moved up and the other is moved down ( like turning a big steering wheel ), the body reacts by tilting to the side, which then begins the twisting rotation.

When it was pointed out to Niven that the Ringworld was dynamically unstable, in that once the center of rotation drifted away from the central sun, gravity would pull the ring into contact with the star, he used this as a plot element in the sequel novel, The Ringworld Engineers.

When an object is not perfectly solid, internal vortices will tend to damp torque-free precession, and the rotation axis will align itself with one of the inertia axes of the body.

When the ski was torqued, the position of the aluminum sheets above and below the axis of rotation required them to slide sideways relative to the core, something that was resisted by the glue along the entire surface of the sheet.

When games move from one region to another, they tend to initially preserve their original sense of rotation ..

When MTV was in its infancy, The Residents ' videos were in heavy rotation since they were among the few music videos available to broadcasters.

When mice still used a mechanical design ( with slotted ' chopper ' wheels interrupting a beam of light to measure rotation ), trackballs had the advantage of being in contact with the user's hand, which is generally cleaner than the desk or mousepad and does not drag lint into the chopper wheels.

When the problem is considered even more closely, the need for a vertical ( parallel to the axis of rotation ) component of the magnetic field arises.

When the coordinates are transformed, for example by rotation or stretching, then the components of the vector also transform.

When using this convention, left or right handedness is determined by pointing one's left or right thumb away from the source, in the same direction that the wave is propagating, and matching the curling of one's fingers to the direction of the temporal rotation of the field at a given point in space.

When determining if the wave is clockwise or counter-clockwise circularly polarized, one again takes the point of view of the source, and while looking away from the source and in the same direction of the wave ’ s propagation, one observes the direction of the field ’ s temporal rotation.

When determining if the wave is clockwise or counter-clockwise circularly polarized, one again takes the point of view of the receiver and, while looking toward the source, against the direction of propagation, one observes the direction of the field ’ s temporal rotation.

* When the subring is isomorphic to the ordinary complex number plane, then g acts as a rotation and preserves the Euclidean angle.

Says Boyd, “ When we heard our video had been relegated to late night rotation, I think that all of us were secretly like, ‘ Yes !’ ”.

When the farmland around their villages became less productive — crop rotation was not practiced — the native people would abandon the site and move to another location.

When the evolved children mentally alter the Moon's rotation and make other planetary manipulations, it becomes too dangerous to remain.

When dealing with the rotation of an object, it becomes simpler to consider the body itself rigid.

When the disk undergoes a full clockwise revolution, the bicycle wheel will not return to its original position, but will have undergone a net rotation of.

When a percentage is referenced with a non-linear taper is relates to the resistance value at the mid-point of the shaft rotation.

When the fingers of the right hand are curled around in the direction of the Rotation of planets | planet's rotation, the thumb points in the direction of the north Geographical pole | pole.

When the fingers of the right hand curl around in the direction of the object's rotation, the thumb points in the direction of its north pole ( from which, looking back at the object, it appears to rotate counter-clockwise ).

When we make one solvent immobile ( by adsorption on a solid support matrix ) and another mobile it results in most common applications of chromatography.

When without his trademark shield, Captain America sometimes uses other shields made from less durable metals such as steel, or even a photonic energy shield designed to mimic a vibranium matrix.

When the determinant is equal to one, the linear mapping defined by the matrix is equi-areal and orientation-preserving.

When separating larger nucleic acids ( greater than a few hundred bases ), the preferred matrix is purified agarose.

When light crosses an optical element the resulting polarization of the emerging light is found by taking the product of the Jones matrix of the optical element and the Jones vector of the incident light.

When the M18A1 is detonated, the explosion drives the matrix forward, out of the mine at a velocity of, at the same time breaking it into individual fragments.

When these cells are transformed by the polyoma virus, higher tyrosine activity is observed in the cellular matrix, which is also correlated to cellular proliferation.

When A is m × n, it is a property of matrix multiplication that

When the observational errors are uncorrelated and the weight matrix, W, is diagonal, these may be written as

When the errors are uncorrelated, it is convenient to simplify the calculations to factor the weight matrix as.

When no time passes, nothing changes: for zero elapsed time, the K matrix is zero except from a state to itself.

When the R matrix obeys detailed balance, the scale of the probabilities can be redefined using the stationary distribution so that they no longer sum to 1:

When multiplying matrices, the elements of the rows in the first matrix are multiplied with corresponding columns in the second matrix ( depicted in the image right ).

When raising an arbitrary matrix ( not necessarily a diagonal matrix ) to a power, it is often helpful to exploit this property by diagonalizing the matrix first.

In the special case that M is a normal matrix, which by definition must be square, the spectral theorem says that it can be unitarily diagonalized using a basis of eigenvectors, so that it can be written for a unitary matrix U and a diagonal matrix D. When M is also positive semi-definite, the decomposition is also a singular value decomposition.

When an orthonormal basis that the vector a is represented in terms of is rotated, a's matrix in the new basis is obtained through multiplying a by a rotation matrix R. This matrix multiplication is just a compact representation of a sequence of dot products.