{"headings":["sec-reeller-vektorraum","vektorraum","vektoraddition-und-skalarmultiplikation-in-mathbbrm","reeller-vektorraum","reeller-vektorraum-1","sec-euklidischer-vektorraum","skalarprodukt-auf-mathbbrm","euklidischer-vektorraum","orthogonalität-und-orthonormalität-von-vektoren","sec-lineare-unabhängigkeit","linearkombination","lineare-unabhängigkeit","lineare-abhängigkeit-von-zwei-vektoren","lineare-abhängigkeit-einer-menge-von-vektoren","sec-vektorraumbasen","lineare-hülle-und-aufspannen","basis","eigenschaften-von-basen","basisdarstellung-und-koordinaten","eindeutigkeit-der-basisdarstellung","orthonormalbasis-von-mathbbrm","kanonische-basis-und-kanonische-einheitsvektoren","sec-selbstkontrollfragen-vektoren","sec-vektoren"],"entries":[{"order":{"section":[9,0,0,0,0,0,0],"number":1},"key":"sec-vektoren"},{"order":{"section":[9,1,0,0,0,0,0],"number":3},"key":"fig-vektorsubtraktion-R2","caption":"Vektorsubtraktion in \\mathbb{R}^2"},{"order":{"section":[9,1,0,0,0,0,0],"number":3},"key":"def-reeller-vektorraum","caption":"Reeller Vektorraum"},{"order":{"section":[9,3,0,0,0,0,0],"number":3},"key":"thm-lineare-abhängigkeit-einer-menge-von-vektoren","caption":"Lineare Abhängigkeit einer Menge von Vektoren"},{"order":{"section":[9,1,0,0,0,0,0],"number":1},"key":"sec-reeller-vektorraum","caption":"9.1 Reeller Vektorraum"},{"order":{"section":[9,5,0,0,0,0,0],"number":1},"key":"eq-xyz","caption":""},{"order":{"section":[9,2,0,0,0,0,0],"number":7},"key":"fig-winkel-R2","caption":"Winkel in \\mathbb{R}^2"},{"order":{"section":[9,3,0,0,0,0,0],"number":9},"key":"def-lineare-unabhängigkeit","caption":"Lineare Unabhängigkeit"},{"order":{"section":[9,4,0,0,0,0,0],"number":4},"key":"thm-eigenschaften-von-basen","caption":"Eigenschaften von Basen"},{"order":{"section":[9,2,0,0,0,0,0],"number":7},"key":"def-orthogonalität-und-orthonormalität-von-vektoren","caption":"Orthogonalität und Orthonormalität von Vektoren"},{"order":{"section":[9,4,0,0,0,0,0],"number":8},"key":"fig-basen-R2","caption":"Zwei Basen von \\mathbb{R}^2"},{"order":{"section":[9,4,0,0,0,0,0],"number":13},"key":"def-orthonormalbasis-von-Rm","caption":"Orthonormalbasis von \\mathbb{R}^m"},{"order":{"section":[9,2,0,0,0,0,0],"number":6},"key":"fig-abstand-R2","caption":"Vektorabstände in \\mathbb{R}^2"},{"order":{"section":[9,1,0,0,0,0,0],"number":1},"key":"thm-reeller-vektorraum","caption":"Reeller Vektorraum"},{"order":{"section":[9,3,0,0,0,0,0],"number":2},"key":"thm-lineare-abhängigkeit-von-zwei-vektoren","caption":"Lineare Abhängigkeit von zwei Vektoren"},{"order":{"section":[9,2,0,0,0,0,0],"number":5},"key":"fig-länge-R2","caption":"Vektorlänge in \\mathbb{R}^2"},{"order":{"section":[9,4,0,0,0,0,0],"number":4},"key":"sec-vektorraumbasen","caption":"9.4 Vektorraumbasen"},{"order":{"section":[9,2,0,0,0,0,0],"number":5},"key":"def-euklidischer-vektorraum","caption":"Euklidischer Vektorraum"},{"order":{"section":[9,1,0,0,0,0,0],"number":2},"key":"def-reelle-vektoraddition-skalarmultiplikation","caption":"Vektoraddition und Skalarmultiplikation in \\mathbb{R}^m"},{"order":{"section":[9,2,0,0,0,0,0],"number":6},"key":"def-länge-abstand-winkel","caption":""},{"order":{"section":[9,1,0,0,0,0,0],"number":1},"key":"fig-vektoren-R2","caption":"Visualisierung von Vektoren in \\mathbb{R}^2"},{"order":{"section":[9,2,0,0,0,0,0],"number":4},"key":"def-skalarprodukt","caption":"Skalarprodukt auf \\mathbb{R}^m"},{"order":{"section":[9,5,0,0,0,0,0],"number":5},"key":"sec-selbstkontrollfragen-vektoren","caption":"9.5 Selbstkontrollfragen"},{"order":{"section":[9,1,0,0,0,0,0],"number":2},"key":"fig-vektoraddition-R2","caption":"Vektoraddition in \\mathbb{R}^2"},{"order":{"section":[9,4,0,0,0,0,0],"number":10},"key":"def-lineare-hülle-und-aufspannen","caption":"Lineare Hülle und Aufspannen"},{"order":{"section":[9,1,0,0,0,0,0],"number":4},"key":"fig-skalarmultiplikation-R2","caption":"Skalarmultiplikation in \\mathbb{R}^2"},{"order":{"section":[9,2,0,0,0,0,0],"number":2},"key":"sec-euklidischer-vektorraum","caption":"9.2 Euklidischer Vektorraum"},{"order":{"section":[9,3,0,0,0,0,0],"number":3},"key":"sec-lineare-unabhängigkeit","caption":"9.3 Lineare Unabhängigkeit"},{"order":{"section":[9,3,0,0,0,0,0],"number":8},"key":"def-linearkombination","caption":"Linearkombination"},{"order":{"section":[9,4,0,0,0,0,0],"number":14},"key":"def-kanonische-basis-und-kanonische-einheitsvektoren","caption":"Kanonische Basis und kanonische Einheitsvektoren"},{"order":{"section":[9,4,0,0,0,0,0],"number":11},"key":"def-basis","caption":"Basis"},{"order":{"section":[9,1,0,0,0,0,0],"number":1},"key":"def-vektorraum","caption":"Vektorraum"},{"order":{"section":[9,4,0,0,0,0,0],"number":12},"key":"def-basisdarstellung-und-koordinaten","caption":"Basisdarstellung und Koordinaten"},{"order":{"section":[9,4,0,0,0,0,0],"number":5},"key":"thm-eindeutigkeit-der-basisdarstellung","caption":"Eindeutigkeit der Basisdarstellung"}],"options":{"chapter-id":"sec-vektoren","chapters":true}}