Sublattice of a lattice
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Show that for any two lattice bases $B in mathbb{R}^{d times k}$ and $C in mathbb{R}^{d times n}$, the first generates a sublattice of the second $(L(B) subseteq L(C))$ if and only if there is an integer matrix $U in mathbb{Z}^{n times k}$ such that $B = CU$.
integer-lattices
asked Jan 25 at 9:58
CharlesCharles
62
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Show that for any two lattice bases $B in mathbb{R}^{d times k}$ and $C in mathbb{R}^{d times n}$, the first generates a sublattice of the second $(L(B) subseteq L(C))$ if and only if there is an integer matrix $U in mathbb{Z}^{n times k}$ such that $B = CU$.
integer-lattices
asked Jan 25 at 9:58
CharlesCharles
62
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This website is not a "do my homework for me" service. What have you tried? Where did you get stuck? What, specifically, do you not understand?
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– Mees de Vries
Jan 25 at 10:18
add a comment |
$begingroup$
Show that for any two lattice bases $B in mathbb{R}^{d times k}$ and $C in mathbb{R}^{d times n}$, the first generates a sublattice of the second $(L(B) subseteq L(C))$ if and only if there is an integer matrix $U in mathbb{Z}^{n times k}$ such that $B = CU$.
integer-lattices
asked Jan 25 at 9:58
CharlesCharles
62
$endgroup$
Show that for any two lattice bases $B in mathbb{R}^{d times k}$ and $C in mathbb{R}^{d times n}$, the first generates a sublattice of the second $(L(B) subseteq L(C))$ if and only if there is an integer matrix $U in mathbb{Z}^{n times k}$ such that $B = CU$.
integer-lattices
integer-lattices
asked Jan 25 at 9:58
CharlesCharles
62
asked Jan 25 at 9:58
CharlesCharles
62
asked Jan 25 at 9:58
CharlesCharles
62
asked Jan 25 at 9:58
CharlesCharles
62
asked Jan 25 at 9:58
CharlesCharles
62
62
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This website is not a "do my homework for me" service. What have you tried? Where did you get stuck? What, specifically, do you not understand?
$endgroup$
– Mees de Vries
Jan 25 at 10:18
add a comment |
$begingroup$
This website is not a "do my homework for me" service. What have you tried? Where did you get stuck? What, specifically, do you not understand?
$endgroup$
– Mees de Vries
Jan 25 at 10:18
$begingroup$
This website is not a "do my homework for me" service. What have you tried? Where did you get stuck? What, specifically, do you not understand?
$endgroup$
– Mees de Vries
Jan 25 at 10:18
$begingroup$
This website is not a "do my homework for me" service. What have you tried? Where did you get stuck? What, specifically, do you not understand?
$endgroup$
– Mees de Vries
Jan 25 at 10:18
add a comment |
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This website is not a "do my homework for me" service. What have you tried? Where did you get stuck? What, specifically, do you not understand?
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– Mees de Vries
Jan 25 at 10:18