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The pattern in which the sample points are distributed in 2 dims, is called a sampling lattice, and can be defined by a generator matrix.. In 2 dimensions, the generator matrix consists of 2 vectors. My Question is how we choose those vectors to produce the sampling matrix? Can two different generator matrix produce the same pattern?

For example, given this enter image description here

enter image description here

i think both of the pair vectors can produce the same sampling matrix

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