stokes (version 1.2-0)

kinner: Inner product of two kforms

Description

Given two k-forms a and b, return the inner product ,<a,b>. Here our underlying vector space V is R^nR^n.

The inner product is a symmetric bilinear form defined in two stages. First, we specify its behaviour on decomposable k-forms =_1_komitted and =_1_komitted as

,=( _i,_j_1 i,j n) omitted

and secondly, we extend to the whole of ^k(V)omitted through linearity.

Usage

kinner(o1,o2,M)

Value

Returns a real number

Arguments

o1,o2

Objects of class kform

M

Matrix

Author

Robin K. S. Hankin

See Also

hodge

Examples

a <- (2*dx)^(3*dy)
b <- (5*dx)^(7*dy)

kinner(a,b)
det(matrix(c(2*5,0,0,3*7),2,2))  # mathematically identical, slight numerical mismatch