cross: Cross products of k-tensors

Description Usage Arguments Details Value Note Author(s) References See Also Examples

Description

\loadmathjax

Cross products of k-tensors

Usage

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

Arguments

U,U1,U2

Object of class ktensor

...

Further arguments, currently ignored

Details

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

\mjdeqn

S\otimes T\left(v_1,...,v_k,v_k+1,..., v_k+l\right)= S\left(v_1,... v_k\right)\cdot T\left(v_k+1,... v_k+l\right).omitted; see latex

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.

Value

The functions documented here all return a spray object.

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

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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

stokes documentation built on Jan. 18, 2022, 1:11 a.m.