cross: Cross products of k-tensors

In wedge: The Exterior Calculus

Description

Cross products of k-tensors

Usage

cross(U, ...)
cross2(U1,U2)

Arguments

U,U1,U2	Object of class ktensor
...	Further arguments, currently ignored

Details

Given a k-tensor object S and an l-tensor T, we can form the cross product S %X% T, defined as

omitted; see PDF

Package idiom for this includes cross(S,T) and S %X% T; note that the cross product is not commutative. Function cross() can take any number of arguments (the result is well-defined because the cross product is associative); it uses cross2() as a low-level helper function.

Note

The binary form %X% uses uppercase X to avoid clashing with %x% which is the Kronecker product in base R.

Author(s)

Robin K. S. Hankin

References

Spivak 1961

See Also

ktensor

Examples

M <- cbind(1:4,2:5)
U1 <- as.ktensor(M,rnorm(4))
U2 <- as.ktensor(t(M),1:2)

cross(U1, U2)
cross(U2, U1)  # not the same!

U1 %X% U2 - U2 %X% U1

wedge documentation built on Sept. 4, 2019, 9:02 a.m.