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[9] [12] Bound vector quantities are formulated as a directed line segment, with a definite initial point besides the magnitude and direction of the main vector. [ 9 ] [ 11 ] For example, a force on the Euclidean plane has two Cartesian components in SI unit of newtons and an accompanying two-dimensional position vector in meters, for a total ...
In linear algebra, a column vector with elements is an matrix [1] consisting of a single column of entries, for example, = [].. Similarly, a row vector is a matrix for some , consisting of a single row of entries, = […]. (Throughout this article, boldface is used for both row and column vectors.)
In a d-dimensional space, Hodge star takes a k-vector to a (d–k)-vector; thus only in d = 3 dimensions is the result an element of dimension one (3–2 = 1), i.e. a vector. For example, in d = 4 dimensions, the cross product of two vectors has dimension 4–2 = 2, giving a bivector. Thus, only in three dimensions does cross product define an ...
The SI unit of the Poynting vector is the watt per square metre (W/m 2); kg/s 3 in base SI units. It is named after its discoverer John Henry Poynting who first derived it in 1884. [1]: 132 Nikolay Umov is also credited with formulating the concept. [2]
"Negative" uniaxial crystals (e.g., calcite CaCO 3, sapphire Al 2 O 3) have n e < n o so for these crystals, the extraordinary axis (optic axis) is the fast axis, whereas for "positive" uniaxial crystals (e.g., quartz SiO 2, magnesium fluoride MgF 2, rutile TiO 2), n e > n o and thus the extraordinary axis (optic axis) is the slow axis. Other ...
The vector potential admitted by a solenoidal field is not unique. If is a vector potential for , then so is +, where is any continuously differentiable scalar function. . This follows from the fact that the curl of the gradient is ze