| linear {evitaicossa} | R Documentation |
Linear functions
Description
Linear functions returning single, double, or triple-symbol aaa
objects.
Usage
linear1(x)
linear2(x)
linear3(x)
Arguments
x |
A numeric vector |
Details
These functions return an antiassociative algebra element with the
specified coefficients. Given a numeric vector v with elements
v_1,v_2,\ldots, v_n then
linear1(v) returns v_1\mathbf{a} + v_2\mathbf{b}+\cdots+
v_n\mathbf{L_n}, where \mathbf{L_n} is the
n^\mathrm{th} letter of the alphabet. Similarly,
linear2(v) returns v_1\mathbf{a}\mathbf{a}+\cdots+
v_n\mathbf{L_n}\mathbf{L_n}, and linear3(v) returns
v_1(\mathbf{a}\mathbf{a})\mathbf{a}+\cdots+
v_n(\mathbf{L_n}\mathbf{L_n})\mathbf{L_n}. They are linear in
the sense that
f(\alpha\mathbf{x}+\beta\mathbf{y})=
\alpha f(\mathbf{x})+\beta f(\mathbf{y})
where \alpha,\beta\in\mathbb{R} and
\mathbf{x},\mathbf{y}\in\mathbb{R}^n.
Value
These functions return an object of class aaa.
Author(s)
Robin K. S. Hankin
Examples
linear1(sample(8))
linear2(sample(8))
linear3(sample(8))
a <- 3
b <- 7
x <- sample(9)
y <- sample(9)
linear1(a*x + b*y) == a*linear1(x) + b*linear1(y)
linear2(a*x + b*y) == a*linear2(x) + b*linear2(y)
linear3(a*x + b*y) == a*linear3(x) + b*linear3(y)