Examples:: *[[Examples]]* Nonexamples:: *[[Nonexamples]]* Constructions:: *[[Constructions|Used in the construction of...]]* Generalizations:: *[[Generalizations]]* Justifications and Intuition:: *[[Justifications and Intuition]]* Properties:: [[determinant as volume of parallelopiped with dimension of the ambient space]] Sufficiencies:: *[[Sufficiencies]]* Equivalences:: *[[Equivalences]]* ---- > [!definition] Definition. ([[parallelopiped]]) > Let $a_{1},\dots,a_{k} \in \rrn$ be [[linearly independent]]. The $k$**-dimensional parallelopiped with edges** $a_{1},\dots,a_{k}$ is the set $\PP = \PP(a_{1}, \dots, a_{k}) = \left\{ \sum_{i=1}^{k} c_{i}a_{i}: 0 \leq c_{i} \leq 1 \right\}.$ (That is, all nonnegative [[linear combination|linear combinations]] of the $as having subunit weights.) ---- #### ---- #### References > [!backlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM [[]] > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ``` > [!frontlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM outgoing([[]]) > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ```