heißt Untervektorraum (UVR) vom , wenn für
• Untervektorraumkriterium
oder
• Durchschnitt
• Vereinigung nicht UVR!!!
• Summe
![[image]](data:image/png;base64,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 "embedded image (png)"){kind=small}
heißt Untervektorraum (UVR) vom ![[image]](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAAPCAIAAACN07NGAAAAA3NCSVQICAjb4U/gAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAvklEQVQokZWSsRHCMAxFBbNwVEzgDXJpqBhBkzCAaBkhfcQiVCi7PIokYBPnuKiU9ez3be8A2Vj7rYCICHO5lgvqAISluZMsAPgygLuPU9P8VBGmkrUKt0Zet0EOx9PzNeT9vrvruam4TSbm4MW2YWm2Yun28Ssg1xJZMrhZ5Hu7lul+8oyhWukfh/YiXT+IDLer5FEqebKjXEU9TEuvuhtAuMf4MmmJrDDj/ZXX95cBt5TqyDpDNQoAO7b/6zdYR8now78zIQAAAABJRU5ErkJggg== "embedded image (png)"){kind=small}
, wenn für heißt Untervektorraum (UVR) vom , wenn für ![[image]](data:image/png;base64,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 "embedded image (png)"){kind=small}
![[image]](data:image/png;base64,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 "embedded image (png)"){kind=small}
![[image]](data:image/png;base64,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 "embedded image (png)"){kind=small}
![[image]](data:image/png;base64,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 "embedded image (png)"){kind=small}
![[image]](data:image/png;base64,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 "embedded image (png)"){kind=small}
![[image]](data:image/png;base64,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 "embedded image (png)"){kind=small}
![[image]](data:image/png;base64,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 "embedded image (png)"){kind=small}