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Hello,

let's say that we have a lattice ##\Lambda##. Now I take one of it's basis vectors say ##b_1## and project all the lattice points onto the line which is orthogonal to ##b_1##, this line could be calculated via Gram-Schmidt for instance. But does this then form a lattice again? It is possible to formalize this a bit more? With my definition of a lattice ##\Lambda = \{\sum \lambda_ib_i, \lambda_i \in \mathbb{Z}\}##, however, I cannot prove that this projection on the line again represents a lattice.

let's say that we have a lattice ##\Lambda##. Now I take one of it's basis vectors say ##b_1## and project all the lattice points onto the line which is orthogonal to ##b_1##, this line could be calculated via Gram-Schmidt for instance. But does this then form a lattice again? It is possible to formalize this a bit more? With my definition of a lattice ##\Lambda = \{\sum \lambda_ib_i, \lambda_i \in \mathbb{Z}\}##, however, I cannot prove that this projection on the line again represents a lattice.

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