The coordinate system most frequently used to quantitatively describe a n-dimensional space.
In 2 dimensions, i.e. a plane, it describes any point as a function of 2 perpendicular unit vectors (1,0) and (0,1) and in 3 dimensions as a function of 3 perpendicular unit vectors (1,0,0), (0,1,0) and (0,0,1). Functions in 2 dimensions are often conveniently described using the so-called theory of functions. When using this type of mathematical description, the imaginary number
i = √(-1) is introduced to label the y-axis.
a + ib is then actually a 2 dimensional vector with a x-axis component of 'a' and a y-axis component of 'b'.
The 'a' is called the real part and the 'b' the imaginary part of the function, an expression that is frequently encountered in MRI, where the real image is a pixel-wise representation of 'a' and the imaginary image a pixel-wise representation of 'b', with 'a' and 'b' the components of the xy-magnetization along the x- and y-axis, respectively.
(Renatus Cartesius/Rene Descartes, 1596-1650, French philosopher and mathematician)

Mathematically, the eigenvalue is the factor by which a linear transformation multiplies one of its eigenvectors. In an appropriate spatial reference frame, the diffusion tensor is diagonal (contains only three nonzero elements). These elements in diffusion tensor imaging are called the eigenvalues. The vectors characterizing the reference frame are the eigenvectors.

The FEER method was the first clinically useful flow quantification method using phase effects, from which all spin phase related flow quantification techniques currently in use are derived.
In this sequence a gradient echo is measured after a gradient with flow compensation. The measured signal phase should be zero for all pixels. A deviation from gradient symmetry by shifting the gradient ramp slightly away from the symmetry condition will impart a defined phase shift to the magnetization vectors associated with spins from pixels with flow.
Slight stable variations in the magnetic field across the imaging volume will prevent the phase angle from being uniformly zero throughout the volume in the flow-compensated image. The first image (acquired without gradient shift) serves as reference, defining the values of all pixel phase angles in the flow (motion) compensated sequence. Ensuing images with gradient phase shifts imparted in each of the 3 spatial axes will then permit measurement of the 3 components of the velocity vector v = (vx, vy, vz) by calculating the respective phases px, py and pz by simply subtracting the pixel phases measured in the compensated image from the 3 images with a well defined velocity sensitization.
The determination of all 3 components of the velocity vector requires the measurement of 4 images.
The phase quantification requires an imaging time four times longer than the simple measurement of a phase image and associated magnitude image. If only one arbitrary flow direction is of interest, it suffices to acquire the reference image plus one image velocity sensitized in the arbitrary direction of interest.

See also Flow Quantification.

A vector quantity given by the vector product of the force and the position vector where the force is applied; for a rotating body, the torque is the product of the moment of inertia and the resulting angular acceleration.

[B₁] A conventional symbol for the radio frequency field strength (another symbol historically used, is H1). In MRI, B1 labels the field produced by the radio frequency coil.
The B1 field is often conceived of two vectors rotating in opposite directions, usually in a plane transverse to B0. At the Larmor frequency, the vector rotating in the same direction as the precessing spins will interact strongly with the spins.