(redirected from 2-vector)



a tensor that is skew-symmetric with respect to any two of its indices. It thus is a tensor with either only covariant indices (subscripts) or only contravariant indices (superscripts), where each index can take on values from 1 to n. Moreover, a component of a p-vector changes sign when any two of the component’s indices are interchanged.

If the degree—that is, the number of indices—of a p-vector is equal to 2, 3…. m, we speak of a 2-vector, 3-vector, …, m-vector, respectively. For example, aij is a covariant 2-vector if aij = — aji, and bjki is a contravariant 3-vector if bijk = —bjik = bjki = —bikj = bkij = —

. If only those comonents of the m-vector

ωi1, i2, …, im

are retained for which i1 < i2 < … < im, P-Vector essential components will remain.

The components of a p-vector can be arranged in a certain way in the form of a rectangular matrix of n rows and columns P-Vector whose rank is called the rank of the p-vector. If a p-vector’s rank is equal to its degree (valency), the p-vector is the exterior product of tensors of degree one and is said to be simple.

References in periodicals archive ?
Just as groups can have representations on vector spaces, 2-groups have representations on 2-vector spaces, but Lie 2-groups typically have few representations on the finite-dimensional 2-vector spaces introduced by Kapranov and Voevodsky.
terms in the quadratic form (23) there are no limits to corresponding 0-vector, 2-vector and 3-vector speeds.
b) for the case of pure 2-vector motion by taking V = = d[x.
1]/dt = 1m/s, there corresponds the 2-vector speed d[x.
z(t) is a 2-vector with components: z(1,t) = OIBD(t) and z(2,t) = ADEX(t)
d(t) is the 2-vector of deterministic variables, with components d(t,1) =1, and d(t,2) =t