#algebra/linear-algebra Examples:: [[isometric matrix]] Nonexamples:: *[[Nonexamples]]* Constructions:: *[[Constructions|Used in the construction of...]]* Specializations:: *[[Specializations]]* Generalizations:: *[[Generalizations]]* Justifications and Intuition:: *[[Justifications and Intuition]]* ---- - Let [[inner product space]] be an [[inner product space|inner product space]] over $\ff$, where $\ff$ denotes $\rr$ or $\cc$; - Let $Q \in$ [[vector space of m-by-n matrices]]. > [!definition] Definition. ([[semi-isometric matrix]]) > We call $Q$ **semi-isometric** if $\|Q_{:,i}\|=1 \ \ \fa i \leq n$ > where $m>n$ and $\langle A_{:,i}, A_{:,j} \rangle =0$ for all $i \neq j$. ---- #### ---- #### 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 > ```