# Lattices and matrix calculations

1. Jan 23, 2014

### senmeis

Hi,

here is a paper about planar antenna arrays:https://www.physicsforums.com/attachment.php?attachmentid=65853&d=1390228379 but I have some questions to lattices and matrix calculations in it.

1. On page 354: „The 2x2 matrix T is defined to be a generator for this array lattice.“
Is this 2x2 matrix T made of two basis vectors on this lattice?

2. Left side on page 354: „By defining A to be an (N-2)xN matrix whose rows span the solution space to:
PR-1x = 0“
I can’t see the exact definition of matrix A. What is the relation between matrix A and PR-1x = 0?

3. Right side on page 354: „Bt then spans the lattice of solutions to Px = 0“
I still can’t understand what is the meaning of „spans the lattice of solutions to Px = 0“.

4. Left side on page 355: ψ = (AR-1At)-1/2 ø
What is the calculation of (Matrix)exp(-1/2) here?

Senmeis