IsUPB

IsUPB
Determines whether or a set of product vectors form a UPB
Other toolboxes required	none
Related functions	MinUPBSize UPB UPBSepDistinguishable
Function category	Distinguishing objects

IsUPB is a function that determines whether or not a given set of product vectors forms an unextendible product basis (UPB).

Syntax

• IU = IsUPB(U,V,W,...)

Argument descriptions

• U,V,W,...: Matrices, each with the same number of columns as each other, whose columns are the local vectors of the supposed UPB.

Examples

The "Tiles" UPB

The following code verifies that the well-known "Tiles" UPB is indeed a UPB:

>> [u,v] = UPB('Tiles') % generate the local vectors of the "Tiles" UPB

u =

    1.0000    0.7071         0         0    0.5774
         0   -0.7071         0    0.7071    0.5774
         0         0    1.0000   -0.7071    0.5774


v =

    0.7071         0         0    1.0000    0.5774
   -0.7071         0    0.7071         0    0.5774
         0    1.0000   -0.7071         0    0.5774

>> IsUPB(u,v)

ans =

     1

However, if we remove the fifth vector from this set, then it is no longer a UPB:

>> IsUPB(u(:,1:4),v(:,1:4))

ans =

     0

Source code

Click here to view this function's source code on github.