Description
M must be a matrix over ZZ or QQ where the source space is the space of the bundle, i.e., the matrix must have $k$ columns if the bundle has rank $k$. Then the new bundle is given on each ray $\rho$ by the following filtration of image$(E,M)^\rho := M(E^\rho)$ :
image$(E,M)^\rho(i) := M(E^\rho(i))$.
i1 : E = tangentBundle hirzebruchFan 2
o1 = {dimension of the variety => 2 }
number of affine charts => 4
number of rays => 4
rank of the vector bundle => 2
o1 : ToricVectorBundleKlyachko

i2 : E = E ** E
o2 = {dimension of the variety => 2 }
number of affine charts => 4
number of rays => 4
rank of the vector bundle => 4
o2 : ToricVectorBundleKlyachko

i3 : M = matrix {{1,0,1,0},{0,1,0,1/1}}
o3 =  1 0 1 0 
 0 1 0 1 
2 4
o3 : Matrix QQ < QQ

i4 : E1 = image(E,M)
o4 = {dimension of the variety => 2 }
number of affine charts => 4
number of rays => 4
rank of the vector bundle => 2
o4 : ToricVectorBundleKlyachko

i5 : details E1
o5 = HashTable{ 1  => ( 1/2 1/2 ,  2 1 )}
 2   1 0 
 0  => ( 0 1 ,  2 1 )
 1   1 0 
 0  => ( 0 1 ,  2 1 )
 1   1 0 
 1  => ( 1 0 ,  2 1 )
 0   0 1 
o5 : HashTable
