lintransform: linear transformations of zonotopes, and vector matroids

In zonohedra: Compute and Plot Zonohedra from Vector Generators

linear transformations of zonotopes, and vector matroids

Description

These functions perform straightforward linear transformations on the generators of a zonotope, and the column vectors of a vector matroid

Usage

## S3 method for class 'zonohedron'
lintransform( x, W )
## S3 method for class 'zonogon'
lintransform( x, W )
## S3 method for class 'matroid'
lintransform( x, W )

Arguments

x	x can be a vector matroid object, as returned from the constructor matroid() that takes a matrix as input.
W	An invertible matrix that matches the rank of x. This invertibility is verified. W can also be a scalar; it is then replaced by that scalar multiplied by the identity matrix of the appropriate rank.

Value

If x is a zonohedron (or zonogon), lintransform(x) returns the zonohedron (or zonogon) whose generators are the generators of x with the matrix W applied on the left side. This function is optimized - it is not necessary to transform the generators and start all over again.

If x is a vector matroid, lintransform(x) returns the matroid whose generators are the generators of x with the matrix W applied on the left side. If x is a matroid, but *not* a vector matroid, it returns the original matroid and prints a warning message.

In case of error, e.g. invalid W, the function prints an error message and returns NULL.

References

Matroid - Wikipedia. https://en.wikipedia.org/w/index.php?title=Matroid&oldid=1086234057

See Also

rank(), matroid()

zonohedra documentation built on April 3, 2025, 8:11 p.m.